Repository: flutter
Issue: Widgets are not interactable when stacked on top of a WebViewWidget in web.
Labels: engine,d: api docs,platform-web,has reproducible steps,P3,found in release: 3.7,found in release: 3.9,team-web,triaged-web

It appears that stacking widget on top of a WebViewWidget does not work in the web version. 
I have also tested this on Android, and there stacking widgets on top of WebViewWidget does appear to work. 
I also tried using another WebView package  [web_browser](https://pub.dev/packages/web_browser), but the same behaviour occurs. 

## Steps to Reproduce

1. Install ~~webview_flutter_web (0.2.2+1)~~ webview_flutter
2. Execute `flutter run` on the code sample using Chrome  (see "Code sample" section below) 
3. Click "Webview with icon test" button
4. Interact with widgets (back button, visibility icon)

**Expected results:** 

Interactivity with the widgets, such as returning when using the back  button, or switching the visibility symbol to a visibility_off symbol. 

**Actual results:** 
No interactivity. The back button sometimes show the "hover over" effect. 

<details>
<summary>Code sample</summary>

```dart
import 'package:flutter/material.dart';
import 'package:webview_flutter/webview_flutter.dart';
// import 'package:web_browser/web_browser.dart';

void main() {
  runApp(const MainApp());
}

class MainApp extends StatelessWidget {
  const MainApp({super.key});

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: Builder(
        builder: (context) => Scaffold(
          body: Center(
            child: Card(
              child: ListTile(
                  title: const Text(
                    'Webview with icon test',
                  ),
                  onTap: () {
                    Navigator.of(context).push(
                      MaterialPageRoute(
                        builder: (BuildContext context) {
                          return const WebViewPage();
                        },
                      ),
                    );
                  }),
            ),
          ),
        ),
      ),
    );
  }
}

class WebViewPage extends StatefulWidget {
  const WebViewPage({Key? key}) : super(key: key);

  @override
  State<WebViewPage> createState() => _WebViewPageState();
}

class _WebViewPageState extends State<WebViewPage> {
  late final WebViewController _controller;

  @override
  void initState() {
    super.initState();
    _controller = WebViewController()
      ..loadRequest(
        Uri.parse('http://flutter.dev'),
      );
  }

  bool visibilityIsPressed = false;
  @override
  Widget build(BuildContext context) {
    final ColorScheme colors = Theme.of(context).colorScheme;

    return Scaffold(
      extendBodyBehindAppBar: true,
      appBar: AppBar(
        iconTheme: IconThemeData(
          color: colors.primary, 
        ),
        backgroundColor: Colors.transparent,
      ),
      body: Stack(
        children: [
          WebViewWidget(controller: _controller),
          // Browser(initialUriString: 'https://flutter.dev/',), //Another package with the same issue
          SafeArea(
            child: Padding(
              padding: const EdgeInsets.symmetric(horizontal: 20),
              child: Column(
                crossAxisAlignment: CrossAxisAlignment.end,
                children: [
                  IconButton(
                    iconSize: 30,
                    icon: (visibilityIsPressed)
                        ? const Icon(Icons.visibility_off_outlined)
                        : const Icon(Icons.visibility_outlined),
                    onPressed: () {
                      setState(() {
                        visibilityIsPressed = !visibilityIsPressed;
                      });
                    },
                  ),
                ],
              ),
            ),
          ),
        ],
      ),
    );
  }
}


```

</details>

<details>
  <summary>Logs</summary>

The verbose log is too long to attach in the text so it is attached as a separate file. 
[run_verbose.txt](https://github.com/flutter/flutter/files/11054355/run_verbose.txt)

```
Analyzing flutter_application_1...                                      
No issues found! (ran in 1.0s)
```


```
[✓] Flutter (Channel stable, 3.7.6, on Ubuntu 22.10 5.14.0-1034-oem, locale en_US.UTF-8)
    • Flutter version 3.7.6 on channel stable at /home/william/snap/flutter/common/flutter
    • Upstream repository https://github.com/flutter/flutter.git
    • Framework revision 12cb4eb7a0 (3 weeks ago), 2023-03-01 10:29:26 -0800
    • Engine revision ada363ee93
    • Dart version 2.19.3
    • DevTools version 2.20.1

[✓] Android toolchain - develop for Android devices (Android SDK version 33.0.2)
    • Android SDK at /home/william/Android/Sdk
    • Platform android-33-ext4, build-tools 33.0.2
    • Java binary at: /snap/android-studio/125/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_EXECUTABLE = /snap/bin/chromium

[✓] Linux toolchain - develop for Linux desktop
    • clang version 10.0.0-4ubuntu1
    • cmake version 3.16.3
    • ninja version 1.10.0
    • pkg-config version 0.29.1
[run_verbose.txt](https://github.com/flutter/flutter/files/11054321/run_verbose.txt)


[✓] Android Studio (version 2021.3)
    • Android Studio at /snap/android-studio/125/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
    • VS Code at /snap/code/current
    • Flutter extension version 3.60.0

[✓] Connected device (2 available)
    • Linux (desktop) • linux  • linux-x64      • Ubuntu 22.10 5.14.0-1034-oem
    • Chrome (web)    • chrome • web-javascript • Chromium 111.0.5563.64 snap

[✓] HTTP Host Availability
    • All required HTTP hosts are available

• No issues found!
```

</details>