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.

dropdown_button/lib/example.dart

@@ -0,0 +1,70 @@
+import 'package:flutter/material.dart';
+
+// Example: the focused code for this app.
+// A DropdownButton that lets the user pick a fruit from a list.
+class Example extends StatefulWidget {
+  const Example({super.key});
+
+  @override
+  State<Example> createState() => _ExampleState();
+}
+
+class _ExampleState extends State<Example> {
+  final List<String> _fruits = [
+    "Apple",
+    "Banana",
+    "Pineapple",
+    "Mango",
+    "Grapes"
+  ];
+
+  late List<DropdownMenuItem<String>> _dropDownMenuItems;
+  late String _selectedFruit;
+
+  @override
+  void initState() {
+    _dropDownMenuItems = buildAndGetDropDownMenuItems(_fruits);
+    _selectedFruit = _dropDownMenuItems[0].value!;
+    super.initState();
+  }
+
+  List<DropdownMenuItem<String>> buildAndGetDropDownMenuItems(
+      List<String> fruits) {
+    List<DropdownMenuItem<String>> items = [];
+    for (String fruit in fruits) {
+      items.add(DropdownMenuItem(value: fruit, child: Text(fruit)));
+    }
+    return items;
+  }
+
+  void changedDropDownItem(String? selectedFruit) {
+    setState(() {
+      _selectedFruit = selectedFruit!;
+    });
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text("DropDown Button Example"),
+      ),
+      body: Container(
+        child: Center(
+          child: Column(
+            crossAxisAlignment: CrossAxisAlignment.center,
+            mainAxisAlignment: MainAxisAlignment.center,
+            children: <Widget>[
+              Text("Please choose a fruit: "),
+              DropdownButton<String>(
+                value: _selectedFruit,
+                items: _dropDownMenuItems,
+                onChanged: changedDropDownItem,
+              )
+            ],
+          ),
+        ),
+      ),
+    );
+  }
+}