Repository: flutter
Issue: WEB - Back navigation with open drawer clears url
Labels: framework,f: routes,platform-web,has reproducible steps,P2,found in release: 3.3,found in release: 3.4,team-web,triaged-web

## Steps to Reproduce
1. Execute `flutter run` on the code sample <!-- (see "Code sample" section below) -->
2. Open the drawer and click on "Page id"
3. On the new page open the drawer and then navigate back with the browser back arrow

This is a bug that I found in all flutter web project, also using MaterialApp.router

**Expected results:** Navigate to the previous route
**Actual results:** The url clears itself and the page won't change


<details>
<summary>Code sample</summary>
also See the repo attached 

```dart
import 'dart:developer';

import 'package:flutter/material.dart';
import 'package:flutter_web_plugins/flutter_web_plugins.dart';
import 'package:test_drawer_flutter/business_page.dart';
import 'package:test_drawer_flutter/login_page.dart';

void main() {
  setUrlStrategy(PathUrlStrategy());
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  // This widget is the root of your application.
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      initialRoute: '/business',
      onGenerateRoute: (settings) {
        late Widget page;
        log(settings.name.toString());
        if (settings.name == '/login') {
          page = const LoginPage();
        } else if (settings.name!.startsWith('/business')) {
          final subRoute =
          settings.name!.substring('/business'.length);
          page = BusinessPage(
            setupPageRoute: subRoute,
          );
        } else {
          throw Exception('Unknown route: ${settings.name}');
        }
        return MaterialPageRoute<dynamic>(
          builder: (context) {
            return page;
          },
          settings: settings,
        );
      },
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: const MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({super.key, required this.title});

  // This widget is the home page of your application. It is stateful, meaning
  // that it has a State object (defined below) that contains fields that affect
  // how it looks.

  // This class is the configuration for the state. It holds the values (in this
  // case the title) provided by the parent (in this case the App widget) and
  // used by the build method of the State. Fields in a Widget subclass are
  // always marked "final".

  final String title;

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _counter = 0;

  void _incrementCounter() {
    setState(() {
      // This call to setState tells the Flutter framework that something has
      // changed in this State, which causes it to rerun the build method below
      // so that the display can reflect the updated values. If we changed
      // _counter without calling setState(), then the build method would not be
      // called again, and so nothing would appear to happen.
      _counter++;
    });
  }

  @override
  Widget build(BuildContext context) {
    // This method is rerun every time setState is called, for instance as done
    // by the _incrementCounter method above.
    //
    // The Flutter framework has been optimized to make rerunning build methods
    // fast, so that you can just rebuild anything that needs updating rather
    // than having to individually change instances of widgets.
    return Scaffold(
      appBar: AppBar(
        // Here we take the value from the MyHomePage object that was created by
        // the App.build method, and use it to set our appbar title.
        title: Text(widget.title),
      ),
      body: Center(
        // Center is a layout widget. It takes a single child and positions it
        // in the middle of the parent.
        child: Column(
          // Column is also a layout widget. It takes a list of children and
          // arranges them vertically. By default, it sizes itself to fit its
          // children horizontally, and tries to be as tall as its parent.
          //
          // Invoke "debug painting" (press "p" in the console, choose the
          // "Toggle Debug Paint" action from the Flutter Inspector in Android
          // Studio, or the "Toggle Debug Paint" command in Visual Studio Code)
          // to see the wireframe for each widget.
          //
          // Column has various properties to control how it sizes itself and
          // how it positions its children. Here we use mainAxisAlignment to
          // center the children vertically; the main axis here is the vertical
          // axis because Columns are vertical (the cross axis would be
          // horizontal).
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            const Text(
              'You have pushed the button this many times:',
            ),
            Text(
              '$_counter',
              style: Theme.of(context).textTheme.headline4,
            ),
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        onPressed: _incrementCounter,
        tooltip: 'Increment',
        child: const Icon(Icons.add),
      ), // This trailing comma makes auto-formatting nicer for build methods.
    );
  }
}
```

</details>

<details>
  <summary>Logs</summary>

flutter doctor -v

  [✓] Flutter (Channel stable, 3.3.0, on macOS 12.5.1 21G83 darwin-arm, locale en-IT)
      • Flutter version 3.3.0 on channel stable at /Users/nicolamazzocato/flutter
      • Upstream repository https://github.com/flutter/flutter.git
      • Framework revision ffccd96b62 (2 days ago), 2022-08-29 17:28:57 -0700
      • Engine revision 5e9e0e0aa8
      • Dart version 2.18.0
      • DevTools version 2.15.0

</details>

https://user-images.githubusercontent.com/86733853/187889548-8246044d-d5df-44b1-94c0-da53960b65c0.mov

[test_drawer_flutter.zip](https://github.com/flutter/flutter/files/9469009/test_drawer_flutter.zip)