Cupertino gallery app (#2715)

Resolves #2519 

Part of the larger effort to bring the samples/repo into a stable and
maintainable condition that _also_ remains useful. See: #2409

## Pre-launch Checklist

- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I have added sample code updates to the [changelog].
- [x] I updated/added relevant documentation (doc comments with `///`).

cupertino_gallery/lib/widgets/sliding_segmented_control_page.dart

@@ -0,0 +1,38 @@
+import 'package:flutter/cupertino.dart';
+
+class SlidingSegmentedControlPage extends StatefulWidget {
+  const SlidingSegmentedControlPage({super.key});
+
+  @override
+  State<SlidingSegmentedControlPage> createState() =>
+      _SlidingSegmentedControlPageState();
+}
+
+class _SlidingSegmentedControlPageState
+    extends State<SlidingSegmentedControlPage> {
+  int? _groupValue = 0;
+
+  @override
+  Widget build(BuildContext context) {
+    return CupertinoPageScaffold(
+      navigationBar: const CupertinoNavigationBar(
+        middle: Text('Sliding Segmented Control'),
+      ),
+      child: Center(
+        child: CupertinoSlidingSegmentedControl<int>(
+          children: const <int, Widget>{
+            0: Text('One'),
+            1: Text('Two'),
+            2: Text('Three'),
+          },
+          onValueChanged: (int? value) {
+            setState(() {
+              _groupValue = value;
+            });
+          },
+          groupValue: _groupValue,
+        ),
+      ),
+    );
+  }
+}