Code sample

import 'package:flutter/material.dart';
import 'package:flutter_web_plugins/url_strategy.dart';

void main() {
  setUrlStrategy(null);
  runApp(const MyApp());
}

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

  @override
  Widget build(BuildContext context) {
    return const MaterialApp(
      title: 'MyApp',
      color: Colors.black,
      home: MyParentWidget(),
    );
  }
}

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

  @override
  State<MyParentWidget> createState() => _MyParentWidgetState();
}

class _MyParentWidgetState extends State<MyParentWidget> {
  @override
  Widget build(BuildContext context) {
    return MyHomePage(
      key: UniqueKey(),
      onBackPressed: () {
        setState(() {});
      },
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({
    required this.onBackPressed,
    super.key,
  });

  final VoidCallback onBackPressed;

  @override
  State<MyHomePage> createState() {
    return _MyHomePageState();
  }
}

class _MyHomePageState extends State<MyHomePage> {
  bool _changed = false;

  @override
  Widget build(BuildContext context) {
    return WillPopScope(
      onWillPop: () => Future(() {
        widget.onBackPressed();
        return false;
      }),
      child: Column(
        mainAxisAlignment: MainAxisAlignment.spaceEvenly,
        children: [
          Text(
            _textForCurrentState(),
            style: const TextStyle(
              color: Colors.black,
              decoration: TextDecoration.none,
            ),
          ),
          ElevatedButton(
            onPressed: () {
              setState(() {
                _changed = !_changed;
              });
            },
            child: const Text("CHANGE"),
          ),
        ],
      ),
    );
  }

  String _textForCurrentState() {
    return _changed ? "CHANGED" : "NOT CHANGED";
  }
}