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

google_signin/lib/main.dart

@@ -1,81 +1,18 @@
-import 'dart:async';
-
-import 'package:firebase_auth/firebase_auth.dart';
 import 'package:flutter/material.dart';
-import 'package:google_sign_in/google_sign_in.dart';
 
-import 'home.dart';
-import 'user.dart';
+import 'example.dart';
 
 void main() {
-  runApp(const App());
+  runApp(const MyApp());
 }
 
-class App extends StatefulWidget {
-  const App({super.key});
-
-  @override
-  AppState createState() => AppState();
-}
-
-class AppState extends State<App> {
-  final GoogleSignIn googleSignIn = GoogleSignIn.instance;
-  late Widget userPage;
-
-  @override
-  void initState() {
-    super.initState();
-    userPage = Home(
-      onSignin: _signin,
-      onLogout: _logout,
-      showLoading: false,
-    );
-  }
-
-  Future<User?> _signin() async {
-    setState(() {
-      userPage = Home(onSignin: null, onLogout: _logout, showLoading: true);
-    });
-    try {
-      await googleSignIn.initialize();
-      final GoogleSignInAccount account = await googleSignIn.authenticate();
-      final GoogleSignInAuthentication auth = account.authentication;
-      final AuthCredential credential = GoogleAuthProvider.credential(
-        idToken: auth.idToken,
-      );
-      final UserCredential authRes =
-          await FirebaseAuth.instance.signInWithCredential(credential);
-      final User? user = authRes.user;
-      if (user == null) return null;
-
-      setState(() {
-        userPage = UserProfile(onLogout: _logout, user: user);
-      });
-
-      return user;
-    } catch (e) {
-      print(e.toString());
-      return null;
-    }
-  }
-
-  Future<void> _logout() async {
-    await googleSignIn.signOut();
-    setState(() {
-      userPage = Home(
-        onSignin: _signin,
-        onLogout: _logout,
-        showLoading: false,
-      );
-    });
-
-    print("Logged Out");
-  }
+class MyApp extends StatelessWidget {
+  const MyApp({super.key});
 
   @override
   Widget build(BuildContext context) {
     return MaterialApp(
-      home: userPage,
+      home: const Example(),
     );
   }
 }