Publish web_embedding (#1777)

## Pre-launch Checklist

- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-devrel
channel on [Discord].

<!-- Links -->
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[CLA]: https://cla.developers.google.com/
[Discord]: https://github.com/flutter/flutter/wiki/Chat
[Contributors Guide]:
https://github.com/flutter/samples/blob/main/CONTRIBUTING.md


Co-authored-by: Mark Thompson
<2554588+MarkTechson@users.noreply.github.com>
Co-authored-by: David Iglesias <ditman@gmail.com>

Co-authored-by: Mark Thompson <2554588+MarkTechson@users.noreply.github.com>
Co-authored-by: David Iglesias <ditman@gmail.com>

web_embedding/ng-flutter/flutter/lib/main.dart

@@ -0,0 +1,73 @@
+// ignore_for_file: avoid_web_libraries_in_flutter
+
+import 'package:flutter/material.dart';
+
+import 'pages/counter.dart';
+import 'pages/dash.dart';
+import 'pages/text.dart';
+
+import 'src/js_interop.dart';
+
+void main() {
+  runApp(const MyApp());
+}
+
+class MyApp extends StatefulWidget {
+  const MyApp({super.key});
+
+  @override
+  State<MyApp> createState() => _MyAppState();
+}
+
+class _MyAppState extends State<MyApp> {
+  final ValueNotifier<DemoScreen> _screen = ValueNotifier<DemoScreen>(DemoScreen.counter);
+  final ValueNotifier<int> _counter = ValueNotifier<int>(0);
+  final ValueNotifier<String> _text = ValueNotifier<String>('');
+
+  late final DemoAppStateManager _state;
+
+  @override
+  void initState() {
+    super.initState();
+    _state = DemoAppStateManager(
+      screen: _screen,
+      counter: _counter,
+      text: _text,
+    );
+    final export = createDartExport(_state);
+
+    // Emit this through the root object of the flutter app :)
+    broadcastAppEvent('flutter-initialized', export);
+  }
+
+  @override
+  void dispose() {
+    super.dispose();
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return MaterialApp(
+      title: 'Element embedding',
+      theme: ThemeData(
+        colorScheme: ColorScheme.fromSeed(seedColor: Colors.blue),
+        useMaterial3: true,
+      ),
+      home: ValueListenableBuilder<DemoScreen>(
+        valueListenable: _screen,
+        builder: (context, value, child) => demoScreenRouter(value),
+      ),
+    );
+  }
+
+  Widget demoScreenRouter(DemoScreen which) {
+    switch (which) {
+      case DemoScreen.counter:
+        return CounterDemo(counter: _counter);
+      case DemoScreen.text:
+        return TextFieldDemo(text: _text);
+      case DemoScreen.dash:
+        return DashDemo(text: _text);
+    }
+  }
+}