This PR adds a `RawMenuAnchor()` widget to widgets.dart. The purpose of
this widget is to provide a menu primitive for the Material and
Cupertino libraries (and others) to build upon. Additionally, this PR
makes MenuController an inherited widget to simplify nested access to
the menu (e.g. if you want to launch a context menu from a deeply-nested
widget).

This PR:
* Centralizes core menu logic to a private class,` _RawMenuAnchor()`, 
  * Provides the internals for interacting with menus:
    * TapRegion interop
    * DismissMenuAction handler
    * Close on scroll/resize
    * Focus traversal information, if applicable
* Subclasses override `_open`, `_close`, `_isOpen`, `_buildAnchor`, and
`_menuScopeNode`
* State is accessible by descendents via
`MenuController.maybeOf(context)._anchor`
* Adds 2 public constructors, backed by a `_RawMenuAnchor()` that
contains shared logic.
  * `RawMenuAnchor()`
    * Users build the overlay from scratch.
* Provides anchor/overlay position information and TapRegionGroupId to
builder
    * Does not provide FocusScope management. 
  * `RawMenuAnchorGroup()`
    * A primitive for menus that do not have overlays (menu bars). 
* This was previously called RawMenuAnchor.node(), but @dkwingsmt made a
good case for splitting out the constructor.

<s>Documentation examples have been added, and can be viewed at
https://menu-anchor.web.app/</s>


<s>https://github.com/user-attachments/assets/25d35f23-2aad-4d07-9172-5c3fd65d53cf</s>

@dkwingsmt 

List which issues are fixed by this PR.
#143712

Some issues that need to be addressed:

Semantics:
<img width="1027" alt="image"
src="https://github.com/user-attachments/assets/d69661c9-8435-4d9c-b200-474968cb57eb">
I'm basing the menu semantics off of the comment
[here](https://github.com/flutter/engine/blob/ef3ca70db20230436b6defe5b4cdb0d242deea96/lib/web_ui/lib/src/engine/semantics/semantics.dart#L382),
but I'm unsure whether the route should be given a name. There is no
menubar/menu/menuitem role in Flutter, so I'm assuming the menu should
be composed of nested dialogs

<s>Unlike the menubar pattern from
[W3C](https://www.w3.org/WAI/ARIA/apg/patterns/menubar/examples/menubar-navigation/),
the RawMenuAnchor

- does not close on tab/shift-tab. I left this behavior out of the menu
so that users could customize tab behavior, but I'm not opinionated
either way
- does not open on ArrowUp/ArrowDown, because this could interfere with
user focus behavior in unconventional menu setups (e.g. a vertical
menu).
- does not automatically focus the first item in a menu overlay when
activated via enter/spacebar, but does focus the first item when
horizontal traversal opens a submenu. Automatically focusing the first
item whenever an overlay opens interferes with hover traversal, and I
couldn't think of a good way to only focus the first item when an
overlay is triggered via enter/spacebar.
- doesn't focus disabled items (I wasn't sure how to address this
without editing MenuItemButton)

While it is possible to nest menus -- for example, a dropdown anchor
within a full-app context menu area -- nested menus behave as a single
group. I was considering adding an additional parameter that separates
nested root menus from their parents, and am interested to hear your
feedback.</s>

*If you had to change anything in the [flutter/tests] repo, include a
link to the migration guide as per the [breaking change policy].*

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md
[test-exempt]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes
[Discord]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md
[Data Driven Fixes]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md

---------

Co-authored-by: Bruno Leroux <[email protected]>
Co-authored-by: chunhtai <[email protected]>

Alternative to #163481,
#167537,
#163481 that uses callbacks.

@dkwingsmt - you inspired me to simplify the menu behavior. I didn't end
up using Actions, mainly because nested behavior was unwieldy and
capturing BuildContext has drawbacks. This uses a basic callback
mechanism to animate the menu open and closed. Check out the examples.

<hr />

### The problem
RawMenuAnchor synchronously shows or hides an overlay menu in response
to `MenuController.open()` and `MenuController.close`, respectively.
Because animations cannot be run on a hidden overlay, there currently is
no way for developers to add animations to RawMenuAnchor and its
subclasses (MenuAnchor, DropdownMenuButton, etc).

### The solution
This PR:
- Adds two callbacks -- `onOpenRequested` and `onCloseRequested` -- to
RawMenuAnchor.
- onOpenRequested is called with a position and a showOverlay callback,
which opens the menu when called.
- onCloseRequested is called with a hideOverlay callback, which hides
the menu when called.

When `MenuController.open()` and `MenuController.close()` are called,
onOpenRequested and onCloseRequested are invoked, respectively.

Precursor for #143416,
#135025,
#143712

## Demo


https://github.com/user-attachments/assets/bb14abca-af26-45fe-8d45-289b5d07dab2

```dart
// Copyright 2014 The Flutter Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

// ignore_for_file: public_member_api_docs

import 'dart:ui' as ui;

import 'package:flutter/material.dart' hide MenuController, RawMenuAnchor, RawMenuOverlayInfo;

import 'raw_menu_anchor.dart';

/// Flutter code sample for a [RawMenuAnchor] that animates a simple menu using
/// [RawMenuAnchor.onOpenRequested] and [RawMenuAnchor.onCloseRequested].
void main() {
  runApp(const App());
}

class Menu extends StatefulWidget {
  const Menu({super.key});

  @OverRide
  State<Menu> createState() => _MenuState();
}

class _MenuState extends State<Menu> with SingleTickerProviderStateMixin {
  late final AnimationController animationController;
  final MenuController menuController = MenuController();

  @OverRide
  void initState() {
    super.initState();
    animationController = AnimationController(
      vsync: this,
      duration: const Duration(milliseconds: 300),
    );
  }

  @OverRide
  void dispose() {
    animationController.dispose();
    super.dispose();
  }

  void _handleMenuOpenRequest(Offset? position, void Function({Offset? position}) showOverlay) {
    // Mount or reposition the menu before animating the menu open.
    showOverlay(position: position);

    if (animationController.isForwardOrCompleted) {
      // If the menu is already open or opening, the animation is already
      // running forward.
      return;
    }

    // Animate the menu into view. This will cancel the closing animation.
    animationController.forward();
  }

  void _handleMenuCloseRequest(VoidCallback hideOverlay) {
    if (!animationController.isForwardOrCompleted) {
      // If the menu is already closed or closing, do nothing.
      return;
    }

    // Animate the menu out of view.
    //
    // Be sure to use `whenComplete` so that the closing animation
    // can be interrupted by an opening animation.
    animationController.reverse().whenComplete(() {
      if (mounted) {
        // Hide the menu after the menu has closed
        hideOverlay();
      }
    });
  }

  @OverRide
  Widget build(BuildContext context) {
    return RawMenuAnchor(
      controller: menuController,
      onOpenRequested: _handleMenuOpenRequest,
      onCloseRequested: _handleMenuCloseRequest,
      overlayBuilder: (BuildContext context, RawMenuOverlayInfo info) {
        final ui.Offset position = info.anchorRect.bottomLeft;
        return Positioned(
          top: position.dy + 5,
          left: position.dx,
          child: TapRegion(
            groupId: info.tapRegionGroupId,
            child: Material(
              color: ColorScheme.of(context).primaryContainer,
              shape: RoundedRectangleBorder(borderRadius: BorderRadius.circular(8)),
              elevation: 3,
              child: SizeTransition(
                sizeFactor: animationController,
                child: const SizedBox(
                  height: 200,
                  width: 150,
                  child: Center(child: Text('Howdy', textAlign: TextAlign.center)),
                ),
              ),
            ),
          ),
        );
      },
      builder: (BuildContext context, MenuController menuController, Widget? child) {
        return FilledButton(
          onPressed: () {
            if (animationController.isForwardOrCompleted) {
              menuController.close();
            } else {
              menuController.open();
            }
          },
          child: const Text('Toggle Menu'),
        );
      },
    );
  }
}

class App extends StatelessWidget {
  const App({super.key});

  @OverRide
  Widget build(BuildContext context) {
    return MaterialApp(
      theme: ThemeData(colorScheme: ColorScheme.fromSeed(seedColor: Colors.blue)),
      home: const Scaffold(body: Center(child: Menu())),
    );
  }
}

```

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md
[test-exempt]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes
[Discord]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md
[Data Driven Fixes]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md

---------

Co-authored-by: Tong Mu <[email protected]>

Alternative to flutter#163481,
flutter#167537,
flutter#163481 that uses callbacks.

@dkwingsmt - you inspired me to simplify the menu behavior. I didn't end
up using Actions, mainly because nested behavior was unwieldy and
capturing BuildContext has drawbacks. This uses a basic callback
mechanism to animate the menu open and closed. Check out the examples.

<hr />

### The problem
RawMenuAnchor synchronously shows or hides an overlay menu in response
to `MenuController.open()` and `MenuController.close`, respectively.
Because animations cannot be run on a hidden overlay, there currently is
no way for developers to add animations to RawMenuAnchor and its
subclasses (MenuAnchor, DropdownMenuButton, etc).

### The solution
This PR:
- Adds two callbacks -- `onOpenRequested` and `onCloseRequested` -- to
RawMenuAnchor.
- onOpenRequested is called with a position and a showOverlay callback,
which opens the menu when called.
- onCloseRequested is called with a hideOverlay callback, which hides
the menu when called.

When `MenuController.open()` and `MenuController.close()` are called,
onOpenRequested and onCloseRequested are invoked, respectively.

Precursor for flutter#143416,
flutter#135025,
flutter#143712

## Demo


https://github.com/user-attachments/assets/bb14abca-af26-45fe-8d45-289b5d07dab2

```dart
// Copyright 2014 The Flutter Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

// ignore_for_file: public_member_api_docs

import 'dart:ui' as ui;

import 'package:flutter/material.dart' hide MenuController, RawMenuAnchor, RawMenuOverlayInfo;

import 'raw_menu_anchor.dart';

/// Flutter code sample for a [RawMenuAnchor] that animates a simple menu using
/// [RawMenuAnchor.onOpenRequested] and [RawMenuAnchor.onCloseRequested].
void main() {
  runApp(const App());
}

class Menu extends StatefulWidget {
  const Menu({super.key});

  @OverRide
  State<Menu> createState() => _MenuState();
}

class _MenuState extends State<Menu> with SingleTickerProviderStateMixin {
  late final AnimationController animationController;
  final MenuController menuController = MenuController();

  @OverRide
  void initState() {
    super.initState();
    animationController = AnimationController(
      vsync: this,
      duration: const Duration(milliseconds: 300),
    );
  }

  @OverRide
  void dispose() {
    animationController.dispose();
    super.dispose();
  }

  void _handleMenuOpenRequest(Offset? position, void Function({Offset? position}) showOverlay) {
    // Mount or reposition the menu before animating the menu open.
    showOverlay(position: position);

    if (animationController.isForwardOrCompleted) {
      // If the menu is already open or opening, the animation is already
      // running forward.
      return;
    }

    // Animate the menu into view. This will cancel the closing animation.
    animationController.forward();
  }

  void _handleMenuCloseRequest(VoidCallback hideOverlay) {
    if (!animationController.isForwardOrCompleted) {
      // If the menu is already closed or closing, do nothing.
      return;
    }

    // Animate the menu out of view.
    //
    // Be sure to use `whenComplete` so that the closing animation
    // can be interrupted by an opening animation.
    animationController.reverse().whenComplete(() {
      if (mounted) {
        // Hide the menu after the menu has closed
        hideOverlay();
      }
    });
  }

  @OverRide
  Widget build(BuildContext context) {
    return RawMenuAnchor(
      controller: menuController,
      onOpenRequested: _handleMenuOpenRequest,
      onCloseRequested: _handleMenuCloseRequest,
      overlayBuilder: (BuildContext context, RawMenuOverlayInfo info) {
        final ui.Offset position = info.anchorRect.bottomLeft;
        return Positioned(
          top: position.dy + 5,
          left: position.dx,
          child: TapRegion(
            groupId: info.tapRegionGroupId,
            child: Material(
              color: ColorScheme.of(context).primaryContainer,
              shape: RoundedRectangleBorder(borderRadius: BorderRadius.circular(8)),
              elevation: 3,
              child: SizeTransition(
                sizeFactor: animationController,
                child: const SizedBox(
                  height: 200,
                  width: 150,
                  child: Center(child: Text('Howdy', textAlign: TextAlign.center)),
                ),
              ),
            ),
          ),
        );
      },
      builder: (BuildContext context, MenuController menuController, Widget? child) {
        return FilledButton(
          onPressed: () {
            if (animationController.isForwardOrCompleted) {
              menuController.close();
            } else {
              menuController.open();
            }
          },
          child: const Text('Toggle Menu'),
        );
      },
    );
  }
}

class App extends StatelessWidget {
  const App({super.key});

  @OverRide
  Widget build(BuildContext context) {
    return MaterialApp(
      theme: ThemeData(colorScheme: ColorScheme.fromSeed(seedColor: Colors.blue)),
      home: const Scaffold(body: Center(child: Menu())),
    );
  }
}

```

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] I followed the [breaking change policy] and added [Data Driven
Fixes] where supported.
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview
[Tree Hygiene]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md
[test-exempt]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement
[CLA]: https://cla.developers.google.com/
[flutter/tests]: https://github.com/flutter/tests
[breaking change policy]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes
[Discord]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md
[Data Driven Fixes]:
https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md

---------

Co-authored-by: Tong Mu <[email protected]>