Fix DecoratedSliver sample code to reflect the description (#148621)

### Demo screenshot

![Screenshot 2024-05-19 at 05 42 35](https://github.com/flutter/flutter/assets/104349824/6b4aec1f-32ab-496e-ab20-458c2051055d)

### Related issue

- Fixes https://github.com/flutter/flutter/issues/145935
- Add test for `examples/api/test/widgets/sliver/decorated_sliver.0_test.dart` as a part of https://github.com/flutter/flutter/issues/130459.

examples/api/lib/widgets/sliver/decorated_sliver.0.dart

@@ -12,6 +12,14 @@ class SliverDecorationExampleApp extends StatelessWidget {
   @override
   Widget build(BuildContext context) {
     return MaterialApp(
+      theme: ThemeData(
+        textTheme: const TextTheme(
+          titleLarge: TextStyle(
+            fontSize: 24,
+            color: Colors.white30,
+          ),
+        ),
+      ),
       home: Scaffold(
         appBar: AppBar(title: const Text('SliverDecoration Sample')),
         body: const SliverDecorationExample(),
@@ -28,6 +36,7 @@ class SliverDecorationExample extends StatelessWidget {
     return CustomScrollView(
       slivers: <Widget>[
         DecoratedSliver(
+          key: const ValueKey<String>('radial-gradient'),
           decoration: const BoxDecoration(
             gradient: RadialGradient(
               center: Alignment(-0.5, -0.6),
@@ -36,21 +45,60 @@ class SliverDecorationExample extends StatelessWidget {
                 Color(0xFFEEEEEE),
                 Color(0xFF111133),
               ],
-              stops: <double>[0.9, 1.0],
+              stops: <double>[0.4, 0.8],
             ),
           ),
           sliver: SliverList(
-            delegate: SliverChildListDelegate(<Widget>[
-               const Text('Goodnight Moon'),
-            ]),
+            delegate: SliverChildListDelegate(
+              <Widget>[
+                SizedBox(
+                  height: 200.0,
+                  child: Center(
+                    child: Text(
+                      'A moon on a night sky',
+                      style: Theme.of(context).textTheme.titleLarge,
+                    ),
+                  ),
+                ),
+              ],
+            ),
           ),
         ),
-        const DecoratedSliver(
-          decoration: BoxDecoration(
-            color: Colors.amber,
-            borderRadius: BorderRadius.all(Radius.circular(50))
+        DecoratedSliver(
+          key: const ValueKey<String>('linear-gradient'),
+          decoration: const BoxDecoration(
+            gradient: LinearGradient(
+              begin: Alignment.topCenter,
+              end: Alignment.bottomCenter,
+              colors: <Color>[
+                Color(0xFF111133),
+                Color(0xFF1A237E),
+                Color(0xFF283593),
+                Color(0xFF3949AB),
+                Color(0xFF3F51B5),
+                Color(0xFF1976D2),
+                Color(0xFF1E88E5),
+                Color(0xFF42A5F5),
+              ],
+            ),
+          ),
+          sliver: SliverList(
+            delegate: SliverChildListDelegate(
+              <Widget>[
+                SizedBox(
+                  height: 500.0,
+                  child: Container(
+                    alignment: Alignment.topCenter,
+                    padding: const EdgeInsets.only(top: 56.0),
+                    child: Text(
+                      'A blue sky',
+                      style: Theme.of(context).textTheme.titleLarge,
+                    ),
+                  ),
+                ),
+              ],
+            ),
           ),
-          sliver: SliverToBoxAdapter(child: SizedBox(height: 300)),
         ),
       ],
     );

examples/api/test/widgets/sliver/decorated_sliver.0_test.dart

@@ -0,0 +1,74 @@
+// 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/sliver/decorated_sliver.0.dart' as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('Verify the texts are displayed', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.SliverDecorationExampleApp(),
+    );
+
+    final Finder moonText = find.text('A moon on a night sky');
+    expect(moonText, findsOneWidget);
+
+    final Finder blueSkyText = find.text('A blue sky');
+    expect(blueSkyText, findsOneWidget);
+  });
+
+  testWidgets('Verify the sliver with key `radial-gradient` has a RadialGradient', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.SliverDecorationExampleApp(),
+    );
+
+    final DecoratedSliver radialDecoratedSliver = tester.widget<DecoratedSliver>(
+      find.byKey(const ValueKey<String>('radial-gradient')),
+    );
+    expect(
+      radialDecoratedSliver.decoration,
+      const BoxDecoration(
+        gradient: RadialGradient(
+          center: Alignment(-0.5, -0.6),
+          radius: 0.15,
+          colors: <Color>[
+            Color(0xFFEEEEEE),
+            Color(0xFF111133),
+          ],
+          stops: <double>[0.4, 0.8],
+        ),
+      ),
+    );
+  });
+
+  testWidgets('Verify that the sliver with key `linear-gradient` has a LinearGradient', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.SliverDecorationExampleApp(),
+    );
+
+    final DecoratedSliver linearDecoratedSliver = tester.widget<DecoratedSliver>(
+      find.byKey(const ValueKey<String>('linear-gradient')),
+    );
+    expect(
+      linearDecoratedSliver.decoration,
+      const BoxDecoration(
+        gradient: LinearGradient(
+          begin: Alignment.topCenter,
+          end: Alignment.bottomCenter,
+          colors: <Color>[
+            Color(0xFF111133),
+            Color(0xFF1A237E),
+            Color(0xFF283593),
+            Color(0xFF3949AB),
+            Color(0xFF3F51B5),
+            Color(0xFF1976D2),
+            Color(0xFF1E88E5),
+            Color(0xFF42A5F5),
+          ],
+        ),
+      ),
+    );
+  });
+}