The `Tooltip` widget lack of correct state management?

## Issue Description
When I use the `Tooltip` widget in my StatefulWidget, it will have the problem of "the state no longer has a context" or "AnimationController methods should not be used after calling dispose.".

I can control the state of my StatefulWidget, but I cannot control the state of `Tooltip`.

## Steps to Reproduce

1. Use the `Tooltip` widget in your StatefulWidget.
2. The `Tooltip` widget can be displayed or hidden according to state variables.
3. Control whether the `Tooltip` widget is displayed by moving in or out of the mouse.
4. Move the mouse quickly on this `Tooltip` widget.

## Phenomena and Error Log

https://user-images.githubusercontent.com/26346560/150251083-8bb575fd-3cb6-47b0-a662-b5dfe51615bf.mp4

```log
[ERROR:flutter/lib/ui/ui_dart_state.cc(209)] Unhandled Exception: 'package:flutter/src/animation/animation_controller.dart': Failed assertion: line 487 pos 7: '_ticker != null': AnimationController.reverse() called after AnimationController.dispose()
AnimationController methods should not be used after calling dispose.
#0      _AssertionError._doThrowNew (dart:core-patch/errors_patch.dart:47:61)
#1      _AssertionError._throwNew (dart:core-patch/errors_patch.dart:36:5)
#2      AnimationController.reverse (package:flutter/src/animation/animation_controller.dart:487:7)
#3      _rootRun (dart:async/zone.dart:1420:47)
#4      _CustomZone.run (dart:async/zone.dart:1328:19)
#5      _CustomZone.runGuarded (dart:async/zone.dart:1236:7)
#6      _CustomZone.bindCallbackGuarded.<anonymous closure> (dart:async/zone.dart:1276:23)
#7      _rootRun (dart:async/zone.dart:1428:13)
#8      _CustomZone.run (dart:async/zone.dart:1328:19)
#9      _CustomZone.bindCallback.<anonymous closure> (dart:async/zone.dart:1260:23)
#10     Timer._createTimer.<anonymous closure> (dart:async-patch/timer_patch.dart:18:15)
#11     _Timer._runTimers (dart:isolate-patch/timer_impl.dart:395:19)
#12     _Timer._handleMessage (dart:isolate-patch/timer_impl.dart:426:5)
#13     _RawReceivePortImpl._handleMessage (dart:isolate-patch/isolate_patch.dart:192:12)
```
or
```log
[ERROR:flutter/lib/ui/ui_dart_state.cc(209)] Unhandled Exception: This widget has been unmounted, so the State no longer has a context (and should be considered defunct).
Consider canceling any active work during "dispose" or using the "mounted" getter to determine if the State is still active.
#0      State.context.<anonymous closure> (package:flutter/src/widgets/framework.dart:909:9)
#1      State.context (package:flutter/src/widgets/framework.dart:915:6)
#2      _TooltipState._createNewEntry (package:flutter/src/material/tooltip.dart:535:7)
#3      _TooltipState.ensureTooltipVisible (package:flutter/src/material/tooltip.dart:517:5)
#4      _rootRun (dart:async/zone.dart:1420:47)
#5      _CustomZone.run (dart:async/zone.dart:1328:19)
#6      _CustomZone.runGuarded (dart:async/zone.dart:1236:7)
#7      _CustomZone.bindCallbackGuarded.<anonymous closure> (dart:async/zone.dart:1276:23)
#8      _rootRun (dart:async/zone.dart:1428:13)
#9      _CustomZone.run (dart:async/zone.dart:1328:19)
#10     _CustomZone.bindCallback.<anonymous closure> (dart:async/zone.dart:1260:23)
#11     Timer._createTimer.<anonymous closure> (dart:async-patch/timer_patch.dart:18:15)
#12     _Timer._runTimers (dart:isolate-patch/timer_impl.dart:395:19)
#13     _Timer._handleMessage (dart:isolate-patch/timer_impl.dart:426:5)
#14     _RawReceivePortImpl._handleMessage (dart:isolate-patch/isolate_patch.dart:192:12)
```

------

<details>
<summary>Sample Code</summary>

```dart
import 'package:flutter/material.dart';

void main() {
  runApp(const MaterialApp(
    title: 'Flutter Demo',
    home: MyHomePage(),
  ));
}

class MyHomePage extends StatelessWidget {

  const MyHomePage({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: [
            const Padding(
              padding: EdgeInsets.only(bottom: 20),
              child: Text("Please move the mouse quickly between the buttons below."),
            ),
            ...List.generate(5, (index) => const Padding(
              padding: EdgeInsets.only(top: 10),
              child: ItemWidget(),
            ))
          ],
        ),
      ),
    );
  }
}


class ItemWidget extends StatefulWidget {
  const ItemWidget({Key? key}) : super(key: key);

  @override
  _ItemWidgetState createState() => _ItemWidgetState();
}

class _ItemWidgetState extends State<ItemWidget> {

  bool _showButton = false;

  @override
  Widget build(BuildContext context) {
    return Container(
      width: 200,
      height: 35,
      color: Colors.black38,
      padding: const EdgeInsets.all(5),
      child: MouseRegion(
        onEnter: (e) => setState(() => _showButton = true),
        onExit: (e) => setState(() => _showButton = false),
        child: Row(
          mainAxisAlignment: MainAxisAlignment.spaceBetween,
          children: [
            const Text("Item"),
            !_showButton ? Container() : Tooltip(
              message: "This is Tooltip message of Button.",
              child: SizedBox(
                width: 80,
                child: ElevatedButton(
                  onPressed: () {},
                  child: const Text("Button"),
                ),
              ),
            )
          ],
        ),
      ),
    );
  }
}
```
</details>

<details>
<summary>flutter doctor -v</summary>

```txt
[✓] Flutter (Channel stable, 2.8.1, on macOS 12.1 21C52 darwin-x64, locale zh-Hans-CN)
    • Flutter version 2.8.1 at /Users/yowfung/Library/Application Support/fvm/versions/stable
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 77d935af4d (5 weeks ago), 2021-12-16 08:37:33 -0800
    • Engine revision 890a5fca2e
    • Dart version 2.15.1
    • Pub download mirror https://pub.flutter-io.cn
    • Flutter download mirror https://storage.flutter-io.cn

[✓] Android toolchain - develop for Android devices (Android SDK version 31.0.0)
    • Android SDK at /Users/yowfung/Library/Android/sdk
    • Platform android-31, build-tools 31.0.0
    • ANDROID_HOME = /Users/yowfung/Library/Android/sdk
    • Java binary at: /Applications/Android Studio.app/Contents/jre/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 11.0.10+0-b96-7281165)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 13.2.1)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • CocoaPods version 1.10.2

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2020.3)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build 11.0.10+0-b96-7281165)

[✓] IntelliJ IDEA Community Edition (version 2021.2.2)
    • IntelliJ at /Applications/IntelliJ IDEA CE.app
    • Flutter plugin version 63.3.3
    • Dart plugin version 212.5632

[✓] VS Code (version 1.57.1)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.25.0

[✓] Proxy Configuration
    • HTTP_PROXY is set
    • NO_PROXY is localhost,0.0.0.0,127.0.0.1,192.168.1.145,192.168.3.36,192.168.*,169.254.*
    • NO_PROXY contains 127.0.0.1
    • NO_PROXY contains localhost

[✓] Connected device (2 available)
    • macOS (desktop) • macos  • darwin-x64     • macOS 12.1 21C52 darwin-x64
    • Chrome (web)    • chrome • web-javascript • Google Chrome 96.0.4664.93

• No issues found!
```
</details>

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The `Tooltip` widget lack of correct state management? #96890

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The `Tooltip` widget lack of correct state management? #96890