Repository: flutter
Issue: [Drawer] Restoration not working for drawer navigation history
Labels: framework,f: material design,has reproducible steps,a: state restoration,found in release: 3.7,found in release: 3.9,team-design,triaged-design


## Steps to Reproduce on Android

1. Enable "Don't keep activities" in developer options
2. Execute `flutter run` on the code sample
3. Open the drawer with the button on the app bar
4. Press the home button on your device
5. Return to the application
6. Press the back button on your device

**Expected results:**

The drawer should have been closed.

**Actual results:**

The application closed.

**Possible reason:**

The drawer uses `LocalHistoryEntry` which is not restorable.

<details>
<summary>Code sample</summary>

```dart
import 'package:flutter/material.dart';

void main() {
  runApp(const MainApp());
}

class MainApp extends StatelessWidget {
  const MainApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      restorationScopeId: 'app',
      home: Scaffold(
        restorationId: 'scaffold',
        drawer: const Drawer(),
        appBar: AppBar(
          title: const Text('Drawer restoration'),
        ),
      ),
    );
  }
}
```

</details>

<details>
  <summary>Logs</summary>

```
Analyzing bug...                                                        
No issues found! (ran in 1.6s)
```

```
[√] Flutter (Channel stable, 3.7.3, on Microsoft Windows [Version 10.0.19045.2604], locale en-US)
    • Flutter version 3.7.3 on channel stable at C:\Users\me\flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 9944297138 (5 weeks ago), 2023-02-08 15:46:04 -0800
    • Engine revision 248290d6d5
    • Dart version 2.19.2
    • DevTools version 2.20.1

[X] Windows Version (Unable to confirm if installed Windows version is 10 or greater)

[√] Android toolchain - develop for Android devices (Android SDK version 33.0.0)
    • Android SDK at C:\Users\me\AppData\Local\Android\sdk
    • Platform android-33, build-tools 33.0.0
    • Java binary at: C:\Program Files\Android\Android Studio\jre\bin\java
    • Java version OpenJDK Runtime Environment (build 11.0.13+0-b1751.21-8125866)
    • All Android licenses accepted.

[√] Chrome - develop for the web
    • Chrome at C:\Program Files\Google\Chrome\Application\chrome.exe

[√] Visual Studio - develop for Windows (Visual Studio Community 2022 17.5.0)
    • Visual Studio at C:\Program Files\Microsoft Visual Studio\2022\Community
    • Visual Studio Community 2022 version 17.5.33414.496
    • Windows 10 SDK version 10.0.22000.0

[√] Android Studio (version 2021.3)
    • Android Studio at C:\Program Files\Android\Android Studio
    • 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 11.0.13+0-b1751.21-8125866)

[√] VS Code (version 1.76.1)
    • VS Code at C:\Users\me\AppData\Local\Programs\Microsoft VS Code
    • Flutter extension version 3.60.0

[√] Connected device (4 available)
    • sdk gphone64 x86 64 (mobile) • emulator-5554 • android-x64    • Android 13 (API 33) (emulator)
    • Windows (desktop)            • windows       • windows-x64    • Microsoft Windows [Version 10.0.19045.2604]
    • Chrome (web)                 • chrome        • web-javascript • Google Chrome 111.0.5563.65
    • Edge (web)                   • edge          • web-javascript • Microsoft Edge 110.0.1587.69

[√] HTTP Host Availability
    • All required HTTP hosts are available

! Doctor found issues in 1 category.
```

</details>