Add test for inherited_theme.0.dart (#149120)

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

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

dev/bots/check_code_samples.dart

@@ -372,7 +372,6 @@ final Set<String> _knownMissingTests = <String>{
   'examples/api/test/widgets/focus_manager/focus_node.unfocus.0_test.dart',
   'examples/api/test/widgets/framework/build_owner.0_test.dart',
   'examples/api/test/widgets/framework/error_widget.0_test.dart',
-  'examples/api/test/widgets/inherited_theme/inherited_theme.0_test.dart',
   'examples/api/test/widgets/autofill/autofill_group.0_test.dart',
   'examples/api/test/widgets/nested_scroll_view/nested_scroll_view_state.0_test.dart',
   'examples/api/test/widgets/scroll_position/scroll_metrics_notification.0_test.dart',

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

@@ -0,0 +1,30 @@
+// 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/inherited_theme/inherited_theme.0.dart'
+    as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets('StreamBuilder listens to internal stream', (WidgetTester tester) async {
+    await tester.pumpWidget(
+      const example.InheritedThemeExampleApp(),
+    );
+
+    expect(find.byType(GestureDetector), findsOne);
+    expect(find.text('Tap Here'), findsOne);
+
+    final DefaultTextStyle bodyDefaultTextStyle = DefaultTextStyle.of(tester.element(find.text('Tap Here')));
+    expect(bodyDefaultTextStyle.style, const TextStyle(fontSize: 48, color: Colors.blue));
+
+    await tester.tap(find.text('Tap Here'));
+    await tester.pumpAndSettle();
+
+    expect(find.text('Hello World'), findsOne);
+
+    final DefaultTextStyle routeDefaultTextStyle = DefaultTextStyle.of(tester.element(find.text('Hello World')));
+    expect(routeDefaultTextStyle.style, const TextStyle(fontSize: 48, color: Colors.blue));
+  });
+}