refactor: split app wrapper from focused example code (multi-file apps)

Convert 17 multi-file apps to the validated pattern: lib/main.dart keeps
only the MaterialApp bootstrap; a new lib/example.dart holds the full entry
screen and focused example code, importing existing supporting files
(screens/, tabs/, services/, models/, widgets/, utils/).

Apps: analytics_integration, animation_example, biometrics, bottom_sheet,
custom_home_drawer, google_signin, grid_layout, handling_routes,
image_editor, scan_qr_code, statless_counter_app, using_bottom_nav_bar,
using_custom_fonts, using_listview, using_listwheelscrollview,
using_platform_adaptive, view_pdf_file

handling_routes/lib/example.dart

@@ -1,7 +1,8 @@
+// Example: A home screen with navigation to an About page via named routes.
 import 'package:flutter/material.dart';
 
-class HomePage extends StatelessWidget {
-  const HomePage({super.key});
+class Example extends StatelessWidget {
+  const Example({super.key});
 
   @override
   Widget build(BuildContext context) {
@@ -26,7 +27,9 @@ class HomePage extends StatelessWidget {
               Text(
                 "Home Page\nClick on below icon to goto About Page",
                 // Setting the style for the Text
-                style: TextStyle(fontSize: 20.0,),
+                style: TextStyle(
+                  fontSize: 20.0,
+                ),
                 // Set text alignment to center
                 textAlign: TextAlign.center,
               ),

handling_routes/lib/main.dart

@@ -1,10 +1,11 @@
 import 'package:flutter/material.dart';
 import 'package:handling_routes/screens/about.dart';
-import 'package:handling_routes/screens/home.dart';
+
+import 'example.dart';
 
 void main() {
   runApp(MaterialApp(
-    home: HomePage(), // home has implicit route set at '/'
+    home: const Example(), // home has implicit route set at '/'
     // Setup routes
     routes: <String, WidgetBuilder>{
       // Set named routes