Repository: flutter
Issue: Flutter widgets handles mouse events when HTML element is fullscreen
Labels: engine,platform-web,has reproducible steps,P2,found in release: 3.7,found in release: 3.10,team-web,triaged-web

### 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. Run the code sample
2. Click the red box so that it goes fullscreen
3. Hover and click on the bottom half of the screen

### Expected results

- The cursor stays normal (not SystemMouseCursors.click)
- Nothing is printed to the console

### Actual results

- The cursor becomes SystemMouseCursors.click
- 'Clicked' is printed to the console

### Code sample

<details><summary>Code sample</summary>

Also available at https://github.com/andreasgan/fullscreen_div_clickthrough

```dart
import 'package:flutter/material.dart';
import 'dart:ui' as ui;
import 'dart:html';

void main() {
  // ignore: undefined_prefixed_name
  ui.platformViewRegistry.registerViewFactory(
      'box',
      (int viewId) => DivElement()
        ..style.width = '100px'
        ..style.height = '100px'
        ..style.background = 'red'
        ..onClick.listen((event) {
          (event.target as DivElement).requestFullscreen();
        }));
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      home: Scaffold(
        body: Column(
          children: [
            const SizedBox(
              height: 100,
              width: 100,
              child: HtmlElementView(viewType: 'box'),
            ),
            Expanded(
              child: MouseRegion(
                cursor: SystemMouseCursors.click,
                child: GestureDetector(
                  onTap: () => debugPrint('Clicked'),
                  child: Container(
                    width: double.infinity,
                    height: double.infinity,
                    color: Colors.amber,
                  ),
                ),
              ),
            ),
          ],
        ),
      ),
    );
  }
}

```

</details>


### Screenshots or Video

<details>
<summary>Screenshots / Video demonstration</summary>


https://user-images.githubusercontent.com/727125/231830983-3820679e-d745-4560-bcac-b48f84ae473d.mov



</details>


### Logs

<details><summary>Logs</summary>

Normal default debug run via vscode

</details>


### Flutter Doctor output

<details><summary>Doctor output</summary>

```console
[✓] Flutter (Channel stable, 3.7.10, on macOS 12.6.1 21G217 darwin-arm64, locale en-NO)
    • Flutter version 3.7.10 on channel stable at /Users/andreasgangso/dev/tools/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 4b12645012 (10 days ago), 2023-04-03 17:46:48 -0700
    • Engine revision ec975089ac
    • Dart version 2.19.6
    • DevTools version 2.20.1

[✓] Android toolchain - develop for Android devices (Android SDK version 33.0.0)
    • Android SDK at /Users/andreasgangso/Library/Android/sdk
    • Platform android-33, build-tools 33.0.0
    • Java binary at: /Applications/Android Studio.app/Contents/jre/Contents/Home/bin/java
    • Java version OpenJDK Runtime Environment (build 11.0.12+0-b1504.28-7817840)
    • All Android licenses accepted.

[✓] Xcode - develop for iOS and macOS (Xcode 14.2)
    • Xcode at /Applications/Xcode.app/Contents/Developer
    • Build 14C18
    • CocoaPods version 1.12.0

[✓] Chrome - develop for the web
    • Chrome at /Applications/Google Chrome.app/Contents/MacOS/Google Chrome

[✓] Android Studio (version 2021.2)
    • Android Studio at /Applications/Android Studio.app/Contents
    • 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 11.0.12+0-b1504.28-7817840)

[✓] VS Code (version 1.77.2)
    • VS Code at /Applications/Visual Studio Code.app/Contents
    • Flutter extension version 3.62.0

[✓] Connected device (2 available)
    • macOS (desktop) • macos  • darwin-arm64   • macOS 12.6.1 21G217 darwin-arm64
    • Chrome (web)    • chrome • web-javascript • Google Chrome 112.0.5615.49

[✓] HTTP Host Availability
    • All required HTTP hosts are available

• No issues found!
```

</details>