Sample code:

import 'package:flutter/material.dart';
import 'package:flutter/services.dart';

void main() {
  runApp(const MainApp());
}

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

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Scaffold(
        body: Listener(
          behavior: HitTestBehavior.opaque,
          onPointerDown: (e) {
            print('RAW: ${RawKeyboard.instance.keysPressed}');
            print('HW: ${HardwareKeyboard.instance.logicalKeysPressed}');
          },
          child: Container(),
        ),
      ),
    );
  }
}

To reproduce, focus the flutter window, hold shift key and click on another window to unfocus flutter window. After that, depress the shift key and click anywhere in the Flutter window.

Expected output (keys currently pressed):

flutter: RAW: {}
flutter: HW: {}

Actual output (raw keyboard has shift key stuck):

flutter: RAW: {LogicalKeyboardKey#df100(keyId: "0x200000102", keyLabel: "Shift Left", debugName: "Shift Left")}
flutter: HW: {}

HW keyboard does not have the shift key pressed anymore, but when you shift+click now, the HW keyboard will not register the shift until keyboard event.

The problem here is, as far as I can tell, that only FlutterKeyboardManager only synchronizes modifiers for FlutterEmbedderKeyResponder, not doing anything for FlutterChannelKeyResponder.