refactor: split app wrapper from focused example code (pilot)

Apply a consistent structure to 5 example apps (simple_material_app,
stateful_widget, dropdown_button, using_gradient, using_tabs):

- lib/main.dart now contains only the app bootstrap: runApp + a const
  MyApp widget wrapping the app in a MaterialApp.
- lib/example.dart holds the full screen (Scaffold, AppBar, and the
  focused code that demonstrates the example feature), marked with a
  '// Example:' banner comment.

This makes it easy to pinpoint the code that teaches each concept while
keeping the wrapping/chrome code uniform and minimal. Review this pilot
before rolling the pattern out to the remaining apps.

stateful_widget/lib/example.dart

@@ -0,0 +1,53 @@
+import 'package:flutter/material.dart';
+
+// Example: the focused code for this app.
+// A StatefulWidget that cycles through a list of strings each time the
+// button is pressed.
+class Example extends StatefulWidget {
+  const Example({super.key});
+
+  @override
+  State<Example> createState() => _ExampleState();
+}
+
+class _ExampleState extends State<Example> {
+  int counter = 0;
+  List<String> strings = ['Flutter', 'is', 'cool', "and", "awesome!"];
+  String displayedString = "Hello World!";
+
+  void onPressOfButton() {
+    setState(() {
+      displayedString = strings[counter];
+      counter = counter < 4 ? counter + 1 : 0;
+    });
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text("Stateful Widget"),
+        backgroundColor: Colors.green,
+      ),
+      body: Container(
+        child: Center(
+          child: Column(
+            mainAxisAlignment: MainAxisAlignment.center,
+            children: <Widget>[
+              Text(displayedString, style: TextStyle(fontSize: 40.0)),
+              Padding(padding: EdgeInsets.all(10.0)),
+              ElevatedButton(
+                style: ElevatedButton.styleFrom(backgroundColor: Colors.red),
+                onPressed: onPressOfButton,
+                child: Text(
+                  "Press me",
+                  style: TextStyle(color: Colors.white),
+                ),
+              )
+            ],
+          ),
+        ),
+      ),
+    );
+  }
+}