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/main.dart

@@ -1,7 +1,12 @@
 import 'package:flutter/material.dart';
 import 'package:supabase_flutter/supabase_flutter.dart';
 import 'package:flutter_dotenv/flutter_dotenv.dart';
+import 'package:flutter_riverpod/flutter_riverpod.dart';
+import 'package:go_router/go_router.dart';
+
 import 'core/constants/supabase_constants.dart';
+import 'core/router/app_router.dart';
+import 'providers/auth_provider.dart';
 
 void main() async {
   WidgetsFlutterBinding.ensureInitialized();
@@ -21,25 +26,143 @@ void main() async {
     debugPrint('Failed to initialize Supabase: $e');
   }
   
-  runApp(const SageApp());
+  runApp(const ProviderScope(child: SageApp()));
 }
 
-class SageApp extends StatelessWidget {
+class SageApp extends ConsumerWidget {
   const SageApp({super.key});
 
   @override
-  Widget build(BuildContext context) {
-    return MaterialApp(
+  Widget build(BuildContext context, WidgetRef ref) {
+    final router = ref.watch(routerProvider);
+    
+    return MaterialApp.router(
       title: 'Sage - Food Inventory Tracker',
+      debugShowCheckedModeBanner: false,
       theme: ThemeData(
         colorScheme: ColorScheme.fromSeed(seedColor: Colors.green),
         useMaterial3: true,
       ),
-      home: const HomePage(),
+      routerConfig: router,
+      builder: (context, child) {
+        // Set up error handling for the entire app
+        return ErrorBoundary(
+          child: child!,
+        );
+      },
     );
   }
 }
 
+/// Error boundary widget for catching and displaying errors
+class ErrorBoundary extends StatelessWidget {
+  final Widget child;
+  
+  const ErrorBoundary({
+    super.key,
+    required this.child,
+  });
+
+  @override
+  Widget build(BuildContext context) {
+    return MaterialApp(
+      debugShowCheckedModeBanner: false,
+      home: child,
+      builder: (context, widget) {
+        ErrorWidget.builder = (FlutterErrorDetails errorDetails) {
+          return CustomErrorWidget(errorDetails: errorDetails);
+        };
+        return widget!;
+      },
+    );
+  }
+}
+
+/// Custom error widget for better error display
+class CustomErrorWidget extends StatelessWidget {
+  final FlutterErrorDetails errorDetails;
+  
+  const CustomErrorWidget({
+    super.key,
+    required this.errorDetails,
+  });
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      backgroundColor: Colors.red[50],
+      appBar: AppBar(
+        title: const Text('Error'),
+        backgroundColor: Colors.red[100],
+      ),
+      body: Center(
+        child: Padding(
+          padding: const EdgeInsets.all(16),
+          child: Column(
+            mainAxisAlignment: MainAxisAlignment.center,
+            children: [
+              const Icon(
+                Icons.error_outline,
+                size: 64,
+                color: Colors.red,
+              ),
+              const SizedBox(height: 16),
+              const Text(
+                'An error occurred',
+                style: TextStyle(
+                  fontSize: 20,
+                  fontWeight: FontWeight.bold,
+                  color: Colors.red,
+                ),
+              ),
+              const SizedBox(height: 8),
+              Text(
+                'Please restart the app and try again.',
+                style: TextStyle(
+                  fontSize: 16,
+                  color: Colors.red[700],
+                ),
+                textAlign: TextAlign.center,
+              ),
+              if (debugMode) ...[
+                const SizedBox(height: 16),
+                Container(
+                  padding: const EdgeInsets.all(8),
+                  decoration: BoxDecoration(
+                    color: Colors.red[100],
+                    borderRadius: BorderRadius.circular(8),
+                  ),
+                  child: Text(
+                    errorDetails.toString(),
+                    style: const TextStyle(
+                      fontSize: 12,
+                      fontFamily: 'monospace',
+                    ),
+                  ),
+                ),
+              ],
+              const SizedBox(height: 24),
+              ElevatedButton(
+                onPressed: () {
+                  // Attempt to restart the app by navigating to splash
+                  GoRouter.of(context).go('/splash');
+                },
+                style: ElevatedButton.styleFrom(
+                  backgroundColor: Colors.red,
+                  foregroundColor: Colors.white,
+                ),
+                child: const Text('Restart App'),
+              ),
+            ],
+          ),
+        ),
+      ),
+    );
+  }
+  
+  bool get debugMode => !const bool.fromEnvironment('dart.vm.product');
+}
+
 class HomePage extends StatelessWidget {
   const HomePage({super.key});