Repository: flutter
Issue: [go_router] Tooltip is not dismissed on navigation with NoTransitionPage when mouse is over
Labels: framework,f: routes,package,has reproducible steps,P2,p: go_router,team-framework,triaged-framework,found in release: 3.13,found in release: 3.14

### Is there an existing issue for this?

- [x] I have searched the [existing issues](https://github.com/flutter/flutter/issues)
- [X] I have read the [guide to filing a bug](https://flutter.dev/docs/resources/bug-reports)

### Steps to reproduce

1. Implement a `MaterialApp.router` using `GoRouter`
2. Create two widgets to represent the pages to be routed and add an `IconButton` with a tooltip on the first page that calls the another page on `onPressed` with `GoRouter.of(context).go()`
3. Configure the routes to these pages on `routerConfig` of `MaterialApp`, using `pageBuilder` and wrap the page widget with `NoTransitionPage`
4. Run the application and press the button while dragging the mouse pointer to the `Tooltip`
5. Once the next page is loaded, if you drag the mouse pointer out of the `Tooltip`, it will stay on a "disappearing" state

It may be easier to reproduce if when the pages have more elements to render or the next page is async loaded (with a backend, for example)

I should mention that is tested this with Flutter v3.12.0 and it does not happen. So, this behavior may be happening after v3.13.0 changes.

### Expected results

The `Tooltip` might be completed dismissed on page navigation

### Actual results

The `Tooltip` freezes while dismissing

### Code sample

<details><summary>Code sample</summary>

```dart
import 'package:flutter/material.dart';
import 'package:go_router/go_router.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp.router(
      title: 'Flutter Demo',
      theme: ThemeData(
        colorScheme: ColorScheme.fromSeed(seedColor: Colors.deepPurple),
        useMaterial3: true,
      ),
      routerConfig: GoRouter(
        initialLocation: '/',
        routes: [
          GoRoute(
            path: "/",
            pageBuilder: (context, state) => const NoTransitionPage(
              child: MyHomePage(
                title: "Page 1",
              ),
            ),
          ),
          GoRoute(
            path: "/second",
            pageBuilder: (context, state) => const NoTransitionPage(
              child: SecondPage(
                title: "Page 2",
              ),
            ),
          )
        ],
      ),
    );
  }
}

class MyHomePage extends StatelessWidget {
  const MyHomePage({super.key, required this.title});

  final String title;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: Theme.of(context).colorScheme.inversePrimary,
        title: Text(title),
      ),
      body: const Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            Text(
              'Page 1',
            ),
          ],
        ),
      ),
      floatingActionButton: IconButton(
        onPressed: () => GoRouter.of(context).go("/second"),
        tooltip: 'Next',
        icon: const Icon(Icons.arrow_forward_ios_rounded),
        style: IconButton.styleFrom(backgroundColor: Colors.black12),
      ),
    );
  }
}

class SecondPage extends StatelessWidget {
  const SecondPage({super.key, required this.title});

  final String title;

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        backgroundColor: Theme.of(context).colorScheme.inversePrimary,
        title: Text(title),
      ),
      body: const Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            Text(
              'Page 2',
            ),
          ],
        ),
      ),
    );
  }
}
```

</details>


### Screenshots or Video

<details>
<summary>Reproducible bug on v3.13.0</summary>

https://github.com/flutter/flutter/assets/20709746/9121d745-6a39-4f2f-8c05-ce64be70434a

</details>

<details>
<summary>Non-reproducible bug on v3.12.0</summary>

https://github.com/flutter/flutter/assets/20709746/78dfa1e1-0004-4b45-8d86-55a9fd7fb4bd

</details>


### Logs

_No response_

### Flutter Doctor output

<details><summary>Doctor output</summary>

```console
[√] Flutter (Channel stable, 3.13.2, on Microsoft Windows [versÆo 10.0.22621.2134], locale pt-BR)
    • Flutter version 3.13.2 on channel stable at C:\flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision ff5b5b5fa6 (13 days ago), 2023-08-24 08:12:28 -0500
    • Engine revision b20183e040
    • Dart version 3.1.0
    • DevTools version 2.25.0

[√] Windows Version (Installed version of Windows is version 10 or higher)

[√] Android toolchain - develop for Android devices (Android SDK version 33.0.2)
    • Android SDK at C:\Users\hendr\AppData\Local\Android\sdk
    • Platform android-33-ext4, build-tools 33.0.2
    • Java binary at: C:\Program Files\Android\Android Studio\jbr\bin\java
    • Java version OpenJDK Runtime Environment (build 11.0.15+0-b2043.56-9505619)
    • All Android licenses accepted.

[√] Chrome - develop for the web
    • Chrome at C:\Program Files\Google\Chrome\Application\chrome.exe

[√] Visual Studio - develop Windows apps (Visual Studio Community 2022 17.6.4)
    • Visual Studio at C:\Program Files\Microsoft Visual Studio\2022\Community
    • Visual Studio Community 2022 version 17.6.33815.320
    • Windows 10 SDK version 10.0.22000.0

[√] Android Studio (version 2022.1)
    • 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 11.0.15+0-b2043.56-9505619)

[√] IntelliJ IDEA Community Edition (version 2022.3)
    • IntelliJ at C:\Program Files\JetBrains\IntelliJ IDEA Community Edition 2022.3.2
    • Flutter plugin version 74.0.3
    • Dart plugin version 223.8888

[√] VS Code (version 1.81.1)
    • VS Code at C:\Users\hendr\AppData\Local\Programs\Microsoft VS Code
    • Flutter extension can be installed from:
       https://marketplace.visualstudio.com/items?itemName=Dart-Code.flutter

[√] Connected device (3 available)
    • Windows (desktop) • windows • windows-x64    • Microsoft Windows [versÆo 10.0.22621.2134]
    • Chrome (web)      • chrome  • web-javascript • Google Chrome 116.0.5845.141
    • Edge (web)        • edge    • web-javascript • Microsoft Edge 116.0.1938.69

[√] Network resources
    • All expected network resources are available.

• No issues found!
```

</details>