Repository: flutter
Issue: [flutter_adaptive_scaffold] Inconsistant "Open navigation drawer" button status
Labels: platform-web,package,team-ecosystem,has reproducible steps,P2,p: flutter_adaptive_scaffold,triaged-ecosystem,found in release: 3.19,found in release: 3.22

### Steps to reproduce

I am constantly displaying the AppBar to have multiple actions available. When the app (web target) is in a large window, with no drawer needed, there is no "Open navigation drawer" button displayed. This is expected as the navigation is displayed in a rail.

When shrinking the window, the navigation rail is hidden, and the navigation should be using the drawer. However, the button for showing the drawer is not displayed.

When refreshing the page (with the small window), the "Open navigation drawer" button appears. However, when enlarging the windows (and making the navigation rail visible), the "Open navigation drawer" button stays visible (and do not trigger any action.

### Expected results

The "Open navigation drawer" button should show and hide depending if the drawer is user for navigation or not (that is, according to the breakpoints).

### Actual results

The "Open navigation drawer" button visibility is not updated according to if the navigation is based on the drawer or on the rail.

### Code sample

<details open><summary>Code sample</summary>

```dart
class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      routes: <String, Widget Function(BuildContext)>{
        ExtractRouteArguments.routeName: (_) => const ExtractRouteArguments()
      },
      debugShowCheckedModeBanner: false,
      home: AdaptiveScaffold(
        destinations: const [
          NavigationDestination(icon: Icon(Icons.abc), label: 'label'),
          NavigationDestination(icon: Icon(Icons.ac_unit), label: 'label'),
        ],
        appBar: AppBar(
          actions: [
            IconButton(
                onPressed: () {}, icon: const Icon(Icons.add_chart_sharp)),
          ],
        ),
        appBarBreakpoint: Breakpoints.standard,
        useDrawer: true,
      ),
    );
  }
}
```

</details>


### Screenshots or Video

<details open>
<summary>Screenshots / Video demonstration</summary>

| Resize operation | Initial state | After resize |
|---|---|---|
| Shrink | ![image](https://github.com/flutter/flutter/assets/149700184/a92134f1-ab66-4581-9b96-d4185428d7ba) | ![image](https://github.com/flutter/flutter/assets/149700184/114d4785-8a80-4a94-9a30-c887de8f408c) |
| Grow | ![image](https://github.com/flutter/flutter/assets/149700184/884be8c7-660d-4de9-874d-3e26b6f0575e) | ![image](https://github.com/flutter/flutter/assets/149700184/c131f751-9702-4067-8f76-500e42ce73f8) |

</details>


### Logs

<details open><summary>Logs</summary>

```console
```

</details>


### Flutter Doctor output

<details open><summary>Doctor output</summary>

```console
[✓] Flutter (Channel stable, 3.19.6, on Microsoft Windows [Version 10.0.22631.3447], locale en-CA)
    • Flutter version 3.19.6 on channel stable at C:\Users\g.surrel\flutter\flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 54e66469a9 (9 days ago), 2024-04-17 13:08:03 -0700
    • Engine revision c4cd48e186
    • Dart version 3.3.4
    • DevTools version 2.31.1

[✓] Windows Version (Installed version of Windows is version 10 or higher)

[✓] Android toolchain - develop for Android devices (Android SDK version 34.0.0)
    • Android SDK at C:\Users\g.surrel\AppData\Local\Android\Sdk
    • Platform android-34, build-tools 34.0.0
    • Java binary at: C:\Program Files\Android\Android Studio\jbr\bin\java
    • Java version OpenJDK Runtime Environment (build 17.0.9+0--11185874)
    • All Android licenses accepted.

[✗] Chrome - develop for the web (Cannot find Chrome executable at .\Google\Chrome\Application\chrome.exe)
    ! Cannot find Chrome. Try setting CHROME_EXECUTABLE to a Chrome executable.

[✓] Visual Studio - develop Windows apps (Visual Studio Build Tools 2022 17.9.6)
    • Visual Studio at C:\Program Files (x86)\Microsoft Visual Studio\2022\BuildTools
    • Visual Studio Build Tools 2022 version 17.9.34728.123
    • Windows 10 SDK version 10.0.22621.0

[✓] Android Studio (version 2023.2)
    • 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 17.0.9+0--11185874)

[✓] VS Code (version 1.88.1)
    • VS Code at C:\Users\g.surrel\AppData\Local\Programs\Microsoft VS Code
    • Flutter extension version 3.86.0

[✓] Connected device (2 available)
    • Windows (desktop) • windows • windows-x64    • Microsoft Windows [Version 10.0.22631.3447]
    • Edge (web)        • edge    • web-javascript • Microsoft Edge 124.0.2478.51

[✓] Network resources
    • All expected network resources are available.

! Doctor found issues in 1 category.
```

</details>