feat(01-11): integrate router into main app with error handling

- Updated main.dart to use ProviderScope and MaterialApp.router
- Integrated AppRouter with proper GoRouter configuration
- Added comprehensive error handling with ErrorBoundary widget
- Updated HomePage to use auth provider for logout functionality
- Fixed SplashPage to use GoRouter navigation
- Implemented router provider for Riverpod integration
- Added proper resource disposal and restart functionality

Files modified:
- lib/main.dart (complete app structure)
- lib/core/router/app_router.dart (router integration)
- lib/features/authentication/presentation/pages/splash_page.dart (navigation fix)
- lib/features/home/presentation/pages/home_page.dart (logout implementation)

lib/features/home/presentation/pages/home_page.dart

@@ -1,6 +1,6 @@
 import 'package:flutter/material.dart';
 import 'package:flutter_riverpod/flutter_riverpod.dart';
-import '../../providers/auth_provider.dart';
+import '../../../providers/auth_provider.dart';
 
 /// Home page for authenticated users
 /// 
@@ -21,8 +21,18 @@ class HomePage extends ConsumerWidget {
           IconButton(
             icon: const Icon(Icons.logout),
             onPressed: () async {
-              // TODO: Implement logout functionality
-              // await ref.read(authStateProvider.notifier).signOut();
+              try {
+                await ref.read(authProvider.notifier).signOut();
+              } catch (e) {
+                if (context.mounted) {
+                  ScaffoldMessenger.of(context).showSnackBar(
+                    SnackBar(
+                      content: Text('Logout failed: ${e.toString()}'),
+                      backgroundColor: Colors.red,
+                    ),
+                  );
+                }
+              }
             },
             tooltip: 'Logout',
           ),