Add test for animated_padding.0.dart API example. (#146718)

This PR contributes to flutter/flutter#130459

### Description
- Adds `examples/api/test/widgets/implicit_animations/animated_padding.0_test.dart` test

Author: ksokolovskyi

dev/bots/check_code_samples.dart

@@ -475,7 +475,6 @@ final Set<String> _knownMissingTests = <String>{
   'examples/api/test/widgets/implicit_animations/animated_fractionally_sized_box.0_test.dart',
   'examples/api/test/widgets/implicit_animations/animated_align.0_test.dart',
   'examples/api/test/widgets/implicit_animations/animated_positioned.0_test.dart',
-  'examples/api/test/widgets/implicit_animations/animated_padding.0_test.dart',
   'examples/api/test/widgets/implicit_animations/sliver_animated_opacity.0_test.dart',
   'examples/api/test/widgets/scroll_view/custom_scroll_view.1_test.dart',
   'examples/api/test/widgets/inherited_notifier/inherited_notifier.0_test.dart',

examples/api/test/widgets/implicit_animations/animated_padding.0_test.dart

@@ -0,0 +1,50 @@
+// 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/implicit_animations/animated_padding.0.dart'
+    as example;
+import 'package:flutter_test/flutter_test.dart';
+
+void main() {
+  testWidgets(
+    'AnimatedPadding animates on ElevatedButton tap',
+    (WidgetTester tester) async {
+      await tester.pumpWidget(
+        const example.AnimatedPaddingExampleApp(),
+      );
+
+      Padding padding = tester.widget(
+        find.descendant(
+          of: find.byType(AnimatedPadding),
+          matching: find.byType(Padding),
+        ),
+      );
+      expect(padding.padding, equals(EdgeInsets.zero));
+
+      await tester.tap(find.byType(ElevatedButton));
+      await tester.pump();
+
+      padding = tester.widget(
+        find.descendant(
+          of: find.byType(AnimatedPadding),
+          matching: find.byType(Padding),
+        ),
+      );
+      expect(padding.padding, equals(EdgeInsets.zero));
+
+      // Advance animation to the end by the 2-second duration specified in
+      // the example app.
+      await tester.pump(const Duration(seconds: 2));
+
+      padding = tester.widget(
+        find.descendant(
+          of: find.byType(AnimatedPadding),
+          matching: find.byType(Padding),
+        ),
+      );
+      expect(padding.padding, equals(const EdgeInsets.all(100.0)));
+    },
+  );
+}