Add ScrollNotificationObserver sample (#127023)

fixes https://github.com/flutter/flutter/issues/126702

### Preview

https://github.com/flutter/flutter/assets/48603081/4c529a0d-b8a5-4950-9095-429f1c5eccbb

examples/api/lib/widgets/scroll_notification_observer/scroll_notification_observer.0.dart

@@ -0,0 +1,135 @@
+// Copyright 2014 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'package:flutter/material.dart';
+
+/// Flutter code sample for [ScrollNotificationObserver].
+
+void main() => runApp(const ScrollNotificationObserverApp());
+
+class ScrollNotificationObserverApp extends StatelessWidget {
+  const ScrollNotificationObserverApp({super.key});
+
+  @override
+  Widget build(BuildContext context) {
+    return MaterialApp(
+      theme: ThemeData(useMaterial3: true),
+      // The Scaffold widget contains a [ScrollNotificationObserver].
+      // This is used by [AppBar] for its scrolled under behavior.
+      //
+      // We can use [ScrollNotificationObserver.maybeOf] to get the
+      // state of this [ScrollNotificationObserver] from descendants
+      // of the Scaffold widget.
+      //
+      // If you're not using a [Scaffold] widget, you can create a  [ScrollNotificationObserver]
+      // to notify its descendants of scroll notifications by adding it to the subtree.
+      home: Scaffold(
+        appBar: AppBar(
+          title: const Text('ScrollNotificationObserver Sample'),
+        ),
+        body: const ScrollNotificationObserverExample(),
+      ),
+    );
+  }
+}
+
+class ScrollNotificationObserverExample extends StatefulWidget {
+  const ScrollNotificationObserverExample({super.key});
+
+  @override
+  State<ScrollNotificationObserverExample> createState() => _ScrollNotificationObserverExampleState();
+}
+
+class _ScrollNotificationObserverExampleState extends State<ScrollNotificationObserverExample> {
+  ScrollNotificationObserverState? _scrollNotificationObserver;
+  ScrollController controller = ScrollController();
+  bool _scrolledDown = false;
+
+  @override
+  void didChangeDependencies() {
+    super.didChangeDependencies();
+    // Remove any previous listener.
+    _scrollNotificationObserver?.removeListener(_handleScrollNotification);
+    // Get the ScrollNotificationObserverState from the Scaffold widget.
+    _scrollNotificationObserver = ScrollNotificationObserver.maybeOf(context);
+    // Add a new listener.
+    _scrollNotificationObserver?.addListener(_handleScrollNotification);
+  }
+
+  @override
+  void dispose() {
+    if (_scrollNotificationObserver != null) {
+      _scrollNotificationObserver!.removeListener(_handleScrollNotification);
+      _scrollNotificationObserver = null;
+    }
+    controller.dispose();
+    super.dispose();
+  }
+
+  void _handleScrollNotification(ScrollNotification notification) {
+    // Check if the notification is a scroll update notification and if the
+    // `notification.depth` is 0. This way we only listen to the scroll
+    // notifications from the closest scrollable, instead of those that may be nested.
+    if (notification is ScrollUpdateNotification && defaultScrollNotificationPredicate(notification)) {
+      final ScrollMetrics metrics = notification.metrics;
+      // Check if the user scrolled down.
+      if (_scrolledDown != metrics.extentBefore > 0) {
+        setState(() {
+          _scrolledDown = metrics.extentBefore > 0;
+        });
+      }
+    }
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Stack(
+      children: <Widget>[
+        SampleList(controller: controller),
+        // Show the button only if the user scrolled down.
+        if (_scrolledDown)
+          Positioned(
+            right: 25,
+            bottom: 20,
+            child: Center(
+              child: GestureDetector(
+                onTap: () {
+                  // Scroll to the top when the user taps the button.
+                  controller.animateTo(0, duration: const Duration(milliseconds: 200), curve:Curves.fastOutSlowIn);
+                },
+                child: const Card(
+                  child: Padding(
+                    padding: EdgeInsets.all(8.0),
+                    child: Column(
+                      children: <Widget>[
+                        Icon(Icons.arrow_upward_rounded),
+                        Text('Scroll to top')
+                      ],
+                    ),
+                  ),
+                ),
+              ),
+            ),
+          ),
+      ],
+    );
+  }
+}
+
+class SampleList extends StatelessWidget {
+  const SampleList({super.key, required this.controller});
+
+  final ScrollController controller;
+
+  @override
+  Widget build(BuildContext context) {
+    return ListView.builder(
+      controller: controller,
+      itemCount: 30,
+      itemBuilder: (BuildContext context, int index) {
+        return ListTile(title: Text('Item $index'));
+      },
+    );
+  }
+}

examples/api/test/widgets/scroll_notification_observer/scroll_notification_observer.0_test.dart

@@ -0,0 +1,31 @@
+// Copyright 2014 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'package:flutter/material.dart';
+import 'package:flutter_api_samples/widgets/scroll_notification_observer/scroll_notification_observer.0.dart' as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('Scroll to top buttons appears when scrolling down', (WidgetTester tester) async {
+    const String buttonText = 'Scroll to top';
+
+    await tester.pumpWidget(
+      const example.ScrollNotificationObserverApp(),
+    );
+
+    expect(find.byType(ScrollNotificationObserver), findsOneWidget);
+    expect(find.text(buttonText), findsNothing);
+
+    // Scroll down.
+    await tester.drag(find.byType(ListView), const Offset(0.0, -300.0));
+    await tester.pumpAndSettle();
+
+    expect(find.text(buttonText), findsOneWidget);
+
+    await tester.tap(find.text(buttonText));
+    await tester.pumpAndSettle();
+
+    expect(find.text(buttonText), findsNothing);
+  });
+}

packages/flutter/lib/src/widgets/scroll_notification_observer.dart

@@ -71,6 +71,15 @@ final class _ListenerEntry extends LinkedListEntry<_ListenerEntry> {
 /// This widget is similar to [NotificationListener]. It supports a listener
 /// list instead of just a single listener and its listeners run
 /// unconditionally, they do not require a gating boolean return value.
+///
+/// {@tool dartpad}
+/// This sample shows a "Scroll to top" button that uses [ScrollNotificationObserver]
+/// to listen for scroll notifications from [ListView]. The button is only visible
+/// when the user has scrolled down. When pressed, the button animates the scroll
+/// position of the [ListView] back to the top.
+///
+/// ** See code in examples/api/lib/widgets/scroll_notification_observer/scroll_notification_observer.0.dart **
+/// {@end-tool}
 class ScrollNotificationObserver extends StatefulWidget {
   /// Create a [ScrollNotificationObserver].
   ///