Add an example for SearchBar (#124992)

This PR is to: 
* Update API doc for `SearchBar`.
* Add an example to show how to use a `SearchBar` as the builder of the `SearchAnchor`.

examples/api/lib/material/search_anchor/search_bar.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 [SearchBar].
+
+void main() => runApp(const SearchBarApp());
+
+class SearchBarApp extends StatefulWidget {
+  const SearchBarApp({super.key});
+
+  @override
+  State<SearchBarApp> createState() => _SearchBarAppState();
+}
+
+class _SearchBarAppState extends State<SearchBarApp> {
+  bool isDark = false;
+
+  @override
+  Widget build(BuildContext context) {
+    final ThemeData themeData = ThemeData(useMaterial3: true, brightness: isDark ? Brightness.dark : Brightness.light);
+
+    return MaterialApp(
+      theme: themeData,
+      home: Scaffold(
+        appBar: AppBar(title: const Text('Search Bar Sample')),
+        body: Padding(
+          padding: const EdgeInsets.all(8.0),
+          child: SearchAnchor(
+            builder: (BuildContext context, SearchController controller) {
+              return SearchBar(
+                controller: controller,
+                padding: const MaterialStatePropertyAll<EdgeInsets>(EdgeInsets.symmetric(horizontal: 16.0)),
+                onTap: () { controller.openView(); },
+                onChanged: (_) { controller.openView(); },
+                leading: const Icon(Icons.search),
+                trailing: <Widget>[
+                  Tooltip(
+                    message: 'Change brightness mode',
+                    child: IconButton(
+                      isSelected: isDark,
+                      onPressed: () {
+                        setState(() {
+                          isDark = !isDark;
+                        });
+                      },
+                      icon: const Icon(Icons.wb_sunny_outlined),
+                      selectedIcon: const Icon(Icons.brightness_2_outlined),
+                    ),
+                  )
+                ],
+              );
+            },
+            suggestionsBuilder: (BuildContext context, SearchController controller) {
+              return List<ListTile>.generate(5, (int index) {
+                final String item = 'item $index';
+                return ListTile(
+                  title: Text(item),
+                  onTap: () {
+                    setState(() {
+                      controller.closeView(item);
+                    });
+                  },
+                );
+              });
+            }),
+        ),
+      ),
+    );
+  }
+}

examples/api/test/material/search_anchor/search_bar.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/material/search_anchor/search_bar.0.dart' as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('Can open search view', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.SearchBarApp(),
+    );
+
+    final Finder searchBarFinder = find.byType(SearchBar);
+    final SearchBar searchBar = tester.widget<SearchBar>(searchBarFinder);
+    expect(find.byIcon(Icons.search), findsOneWidget);
+    expect(searchBar.trailing, isNotEmpty);
+    expect(searchBar.trailing?.length, equals(1));
+    final Finder trailingButtonFinder = find.widgetWithIcon(IconButton, Icons.wb_sunny_outlined);
+    expect(trailingButtonFinder, findsOneWidget);
+
+    await tester.tap(trailingButtonFinder);
+    await tester.pumpAndSettle();
+
+    expect(find.widgetWithIcon(IconButton, Icons.brightness_2_outlined), findsOneWidget);
+
+    await tester.tap(searchBarFinder);
+    await tester.pumpAndSettle();
+
+    expect(find.text('item 0'), findsOneWidget);
+    expect(find.text('item 1'), findsOneWidget);
+    expect(find.text('item 2'), findsOneWidget);
+    expect(find.text('item 3'), findsOneWidget);
+    expect(find.text('item 4'), findsOneWidget);
+  });
+}

packages/flutter/lib/src/material/search_anchor.dart

@@ -970,9 +970,13 @@ class SearchController extends TextEditingController {
 
 /// A Material Design search bar.
 ///
-/// Search bars include a [leading] Search icon, a text input field and optional
-/// [trailing] icons. A search bar is typically used to open a search view.
-/// It is the default trigger for a search view.
+/// A [SearchBar] looks like a [TextField]. Tapping a SearchBar typically shows a
+/// "search view" route: a route with the search bar at the top and a list of
+/// suggested completions for the search bar's text below. [SearchBar]s are
+/// usually created by a [SearchAnchor.builder]. The builder provides a
+/// [SearchController] that's used by the search bar's [SearchBar.onTap] or
+/// [SearchBar.onChanged] callbacks to show the search view and to hide it
+/// when the user selects a suggestion.
 ///
 /// For [TextDirection.ltr], the [leading] widget is on the left side of the bar.
 /// It should contain either a navigational action (such as a menu or up-arrow)
@@ -982,6 +986,21 @@ class SearchController extends TextEditingController {
 /// the search bar. Typically only one or two action icons are included.
 /// These actions can represent additional modes of searching (like voice search),
 /// a separate high-level action (such as current location) or an overflow menu.
+///
+/// {@tool dartpad}
+/// This example demonstrates how to use a [SearchBar] as the return value of the
+/// [SearchAnchor.builder] property. The [SearchBar] also includes a leading search
+/// icon and a trailing action to toggle the brightness.
+///
+/// ** See code in examples/api/lib/material/search_anchor/search_bar.0.dart **
+/// {@end-tool}
+///
+/// See also:
+///
+/// * [SearchAnchor], a widget that typically uses an [IconButton] or a [SearchBar]
+/// to manage a "search view" route.
+/// * [SearchBarTheme], a widget that overrides the default configuration of a search bar.
+/// * [SearchViewTheme], a widget that overrides the default configuration of a search view.
 class SearchBar extends StatefulWidget {
   /// Creates a Material Design search bar.
   const SearchBar({