Add some cross references in the docs, move an example to a dartpad example (#145571)

## Description

This adds some "See also" links to some docs for `TweenAnimationBuilder` and `ValueListenableBuilder`.

Also, moved a "snippet" example in `ValueListenableBuilder` into the examples directory as a Dartpad example.

## Tests
 - Added test for the example.

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

+// 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 [ValueListenableBuilder].
+
+void main() => runApp(const ValueListenableBuilderExampleApp());
+
+class ValueListenableBuilderExampleApp extends StatelessWidget {
+  const ValueListenableBuilderExampleApp({super.key});
+
+  @override
+  Widget build(BuildContext context) {
+    return const MaterialApp(
+      home: ValueListenableBuilderExample(),
+    );
+  }
+}
+
+class ValueListenableBuilderExample extends StatefulWidget {
+  const ValueListenableBuilderExample({super.key});
+
+  @override
+  State<ValueListenableBuilderExample> createState() => _ValueListenableBuilderExampleState();
+}
+
+class _ValueListenableBuilderExampleState extends State<ValueListenableBuilderExample> {
+  final ValueNotifier<int> _counter = ValueNotifier<int>(0);
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('ValueListenableBuilder Sample'),
+      ),
+      body: Center(
+        child: Column(
+          mainAxisAlignment: MainAxisAlignment.center,
+          children: <Widget>[
+            const Text('You have pushed the button this many times:'),
+            ValueListenableBuilder<int>(
+              builder: (BuildContext context, int value, Widget? child) {
+                // This builder will only get called when the _counter
+                // is updated.
+                return Row(
+                  mainAxisAlignment: MainAxisAlignment.center,
+                  crossAxisAlignment: CrossAxisAlignment.start,
+                  children: <Widget>[
+                    CountDisplay(count: value),
+                    child!,
+                  ],
+                );
+              },
+              valueListenable: _counter,
+              // The child parameter is most helpful if the child is
+              // expensive to build and does not depend on the value from
+              // the notifier.
+              child: const Padding(
+                padding: EdgeInsets.all(10.0),
+                child: SizedBox(
+                  width: 40,
+                  height: 40,
+                  child: FlutterLogo(size: 40),
+                ),
+              ),
+            ),
+          ],
+        ),
+      ),
+      floatingActionButton: FloatingActionButton(
+        child: const Icon(Icons.plus_one),
+        onPressed: () => _counter.value += 1,
+      ),
+    );
+  }
+}
+
+class CountDisplay extends StatelessWidget {
+  const CountDisplay({super.key, required this.count});
+
+  final int count;
+
+  @override
+  Widget build(BuildContext context) {
+    return Container(
+      width: 100,
+      height: 100,
+      padding: const EdgeInsetsDirectional.all(10),
+      child: Text('$count', style: Theme.of(context).textTheme.headline4),
+    );
+  }
+}

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

+// 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/value_listenable_builder/value_listenable_builder.0.dart' as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('Tapping FAB increments counter', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const MaterialApp(
+        home: example.ValueListenableBuilderExample(),
+      ),
+    );
+
+    String getCount() {
+      return (tester.widget(
+        find.descendant(
+          of: find.byType(example.CountDisplay),
+          matching: find.byType(Text),
+        ),
+      ) as Text).data!;
+    }
+
+    expect(find.text('You have pushed the button this many times:'), findsOneWidget);
+    expect(find.text('0'), findsOneWidget);
+    expect(find.byIcon(Icons.plus_one), findsOneWidget);
+    expect(getCount(), equals('0'));
+
+    await tester.tap(find.byType(FloatingActionButton).first);
+    await tester.pumpAndSettle();
+    expect(getCount(), equals('1'));
+  });
+}

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

@@ -90,6 +90,11 @@ import 'value_listenable_builder.dart';
 /// [AnimatedBuilder], which can be used similarly to this
 /// [TweenAnimationBuilder], but unlike the latter it is powered by a
 /// developer-managed [AnimationController].
+///
+/// See also:
+///
+/// * [ValueListenableBuilder], a widget whose content stays synced with a
+///   [ValueListenable] instead of a [Tween].
 class TweenAnimationBuilder<T extends Object?> extends ImplicitlyAnimatedWidget {
   /// Creates a [TweenAnimationBuilder].
   ///

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

@@ -40,63 +40,11 @@ typedef ValueWidgetBuilder<T> = Widget Function(BuildContext context, T value, W
 /// Using this pre-built child is entirely optional, but can improve
 /// performance significantly in some cases and is therefore a good practice.
 ///
-/// {@tool snippet}
-///
+/// {@tool dartpad}
 /// This sample shows how you could use a [ValueListenableBuilder] instead of
-/// setting state on the whole [Scaffold] in the default `flutter create` app.
-///
-/// ```dart
-/// class MyHomePage extends StatefulWidget {
-///   const MyHomePage({super.key, required this.title});
-///   final String title;
-///
-///   @override
-///   State<MyHomePage> createState() => _MyHomePageState();
-/// }
+/// setting state on the whole [Scaffold] in a counter app.
 ///
-/// class _MyHomePageState extends State<MyHomePage> {
-///   final ValueNotifier<int> _counter = ValueNotifier<int>(0);
-///   final Widget goodJob = const Text('Good job!');
-///   @override
-///   Widget build(BuildContext context) {
-///     return Scaffold(
-///       appBar: AppBar(
-///         title: Text(widget.title)
-///       ),
-///       body: Center(
-///         child: Column(
-///           mainAxisAlignment: MainAxisAlignment.center,
-///           children: <Widget>[
-///             const Text('You have pushed the button this many times:'),
-///             ValueListenableBuilder<int>(
-///               builder: (BuildContext context, int value, Widget? child) {
-///                 // This builder will only get called when the _counter
-///                 // is updated.
-///                 return Row(
-///                   mainAxisAlignment: MainAxisAlignment.spaceEvenly,
-///                   children: <Widget>[
-///                     Text('$value'),
-///                     child!,
-///                   ],
-///                 );
-///               },
-///               valueListenable: _counter,
-///               // The child parameter is most helpful if the child is
-///               // expensive to build and does not depend on the value from
-///               // the notifier.
-///               child: goodJob,
-///             )
-///           ],
-///         ),
-///       ),
-///       floatingActionButton: FloatingActionButton(
-///         child: const Icon(Icons.plus_one),
-///         onPressed: () => _counter.value += 1,
-///       ),
-///     );
-///   }
-/// }
-/// ```
+/// ** See code in examples/api/lib/widgets/value_listenable_builder/value_listenable_builder.0.dart **
 /// {@end-tool}
 ///
 /// See also:
@@ -108,6 +56,8 @@ typedef ValueWidgetBuilder<T> = Widget Function(BuildContext context, T value, W
 ///    you have a direct reference to.
 ///  * [StreamBuilder], where a builder can depend on a [Stream] rather than
 ///    a [ValueListenable] for more advanced use cases.
+///  * [TweenAnimationBuilder], which can animate values in a widget based on a
+///    [Tween].
 class ValueListenableBuilder<T> extends StatefulWidget {
   /// Creates a [ValueListenableBuilder].
   ///