Demonstrate bug in Flutter where usage of "TransitionPage" doesn't change the page, but "MaterialPage" does

flutter_bug_in_transition.dart

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp(),);
}

class MyApp extends StatelessWidget {
  MyApp({super.key}) : _routerDelegate = AppRouterDelegate();
  final RouterDelegate<AppState> _routerDelegate;

  @override
  Widget build(BuildContext context) => 
    MaterialApp.router(
      title: 'Test',
      routerDelegate: _routerDelegate,
      routeInformationParser: AppRouteInformationParser(),
      backButtonDispatcher: RootBackButtonDispatcher(),
    );
}

class AppRouteInformationParser extends RouteInformationParser<AppState> {

  @override
  Future<AppState> parseRouteInformation(RouteInformation routeInformation) {
    final AppState configuration = AppState();
    final uri = Uri.parse(routeInformation.location!);

    if (uri.pathSegments.isEmpty) {
        configuration.home = null;
    } else if (uri.pathSegments.length == 1 && uri.pathSegments.first == 'true') { 
        configuration.home = true;
    } else {
      configuration.home = false;
    }

    return Future.value(configuration);
  }

  @override 
  RouteInformation? restoreRouteInformation(AppState configuration) => 
    RouteInformation(location: configuration.home == null ? "/" : "/${configuration.home}",);
}

class AppRouterDelegate extends RouterDelegate<AppState> with ChangeNotifier, PopNavigatorRouterDelegateMixin<AppState> {

  @override
  final GlobalKey<NavigatorState> navigatorKey;

  AppRouterDelegate() : navigatorKey = GlobalKey<NavigatorState>();

  @override
  Widget build(final BuildContext context) =>
    Navigator(
      key: navigatorKey,
      pages: [
        if(_configuration?.home ?? false)
          TransitionPage(child: SomeScreen("Home", _configuration, key: const ValueKey('home')),)
        else
          //uncomment me:
          //MaterialPage(child: SomeScreen("Other", _configuration, key: const  ValueKey('other')),)
          //comment me:
          TransitionPage(child: SomeScreen("Other", _configuration, key: const  ValueKey('other')),)

      ],
      onPopPage: (route, result) {
        if (!route.didPop(result)) {
          return false;
        }
        
        _configuration?._home = ! (_configuration?._home ?? false);
        return true;
      },
    );

  AppState? _configuration;
  @override
  AppState? get currentConfiguration => _configuration;

  @override
  Future<void> setNewRoutePath(final AppState configuration) async {
    _configuration?.removeListener(notifyListeners);
    _configuration = configuration;
    _configuration?.addListener(notifyListeners);
  }
}

class TransitionPage extends Page {
  final Widget child;
  const TransitionPage({required this.child, super.key});

  @override
  Route createRoute(BuildContext context) {
    return PageRouteBuilder(
      settings: this,
      pageBuilder: (context, animation, animation2) {
        final tween = Tween(begin: const Offset(0.0, 1.0), end: Offset.zero);
        final curveTween = CurveTween(curve: Curves.easeInOut);
        return SlideTransition(
          position: animation.drive(curveTween).drive(tween),
          child: child,
        );
      },
    );
  }
}

class SomeScreen extends StatelessWidget {
  const SomeScreen(this.text, this._appState, {super.key});
  final String text;
  final AppState? _appState;

  @override
  Widget build(BuildContext context) =>
    Scaffold(
      appBar: AppBar(),
      body: Column(children: [
        Text(text),
        ElevatedButton(
          onPressed: () {
            _appState?.home = !(_appState?.home ?? false);
          },
          child: const Text("click me"))
      ],)
    ); 
}

class AppState extends ChangeNotifier {
  bool? _home = false;

  bool? get home => _home;

  set home(bool? home) {
    _home = home;
    notifyListeners();
  }
}