Add test for page_storage.0.dart (#157770)

Contributes to https://github.com/flutter/flutter/issues/130459

It adds a test for
- `examples/api/lib/widgets/page_storage/page_storage.0.dart`

dev/bots/check_code_samples.dart

@@ -314,7 +314,6 @@ final Set<String> _knownMissingTests = <String>{
   'examples/api/test/widgets/media_query/media_query_data.system_gesture_insets.0_test.dart',
   'examples/api/test/widgets/image/image.frame_builder.0_test.dart',
   'examples/api/test/widgets/image/image.loading_builder.0_test.dart',
-  'examples/api/test/widgets/page_storage/page_storage.0_test.dart',
   'examples/api/test/widgets/scrollbar/raw_scrollbar.1_test.dart',
   'examples/api/test/widgets/scrollbar/raw_scrollbar.2_test.dart',
   'examples/api/test/widgets/scrollbar/raw_scrollbar.desktop.0_test.dart',

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

@@ -0,0 +1,39 @@
+// 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/page_storage/page_storage.0.dart' as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('Can choose to stay on page', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.PageStorageExampleApp(),
+    );
+
+    expect(find.widgetWithText(AppBar, 'Persistence Example'), findsOne);
+
+    expect(find.text('0'), findsOne);
+
+    await tester.scrollUntilVisible(find.text('10'), 100);
+
+    expect(find.text('0'), findsNothing);
+
+    await tester.tap(find.byIcon(Icons.settings));
+    await tester.pumpAndSettle();
+
+    expect(find.text('0'), findsOne);
+    await tester.scrollUntilVisible(find.text('20'), 100);
+
+    await tester.tap(find.byIcon(Icons.home));
+    await tester.pumpAndSettle();
+
+    expect(find.text('10'), findsOne);
+
+    await tester.tap(find.byIcon(Icons.settings));
+    await tester.pumpAndSettle();
+
+    expect(find.text('20'), findsOne);
+  });
+}