feat: implement Iteration 2 — product management

Backend:
- migrations/005: add pg_trgm extension + search indexes on ingredient_mappings
- migrations/006: products table with computed expires_at column
- ingredient: add Search method (aliases + ILIKE + trgm) + HTTP handler
- product: full package — model, repository (CRUD + BatchCreate + ListForPrompt), handler
- gemini: add AvailableProducts field to RecipeRequest, include in prompt
- recommendation: add ProductLister interface, load user products for personalised prompts
- server/main: wire ingredient and product handlers with new routes

Flutter:
- models: Product, IngredientMapping with json_serializable
- ProductService: getProducts, createProduct, updateProduct, deleteProduct, searchIngredients
- ProductsNotifier: create/update/delete with optimistic delete
- ProductsScreen: expiring-soon section, normal section, swipe-to-delete, edit bottom sheet
- AddProductScreen: name field with 300ms debounce autocomplete, qty/unit/days fields
- app_router: /products/add route + Badge on Products nav tab showing expiring count
- MainShell converted to ConsumerWidget for badge reactivity

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

client/lib/core/router/app_router.dart

@@ -7,10 +7,12 @@ import '../../features/auth/login_screen.dart';
 import '../../features/auth/register_screen.dart';
 import '../../features/home/home_screen.dart';
 import '../../features/products/products_screen.dart';
+import '../../features/products/add_product_screen.dart';
 import '../../features/menu/menu_screen.dart';
 import '../../features/recipes/recipe_detail_screen.dart';
 import '../../features/recipes/recipes_screen.dart';
 import '../../features/profile/profile_screen.dart';
+import '../../features/products/product_provider.dart';
 import '../../shared/models/recipe.dart';
 import '../../shared/models/saved_recipe.dart';
 
@@ -48,10 +50,14 @@ final routerProvider = Provider<GoRouter>((ref) {
           if (extra is SavedRecipe) {
             return RecipeDetailScreen(saved: extra);
           }
-          // Fallback: pop back if navigated without a valid extra.
           return const _InvalidRoute();
         },
       ),
+      // Add product — shown without the bottom navigation bar.
+      GoRoute(
+        path: '/products/add',
+        builder: (_, __) => const AddProductScreen(),
+      ),
       ShellRoute(
         builder: (context, state, child) => MainShell(child: child),
         routes: [
@@ -82,7 +88,7 @@ class _InvalidRoute extends StatelessWidget {
   }
 }
 
-class MainShell extends StatelessWidget {
+class MainShell extends ConsumerWidget {
   final Widget child;
 
   const MainShell({super.key, required this.child});
@@ -96,26 +102,46 @@ class MainShell extends StatelessWidget {
   ];
 
   @override
-  Widget build(BuildContext context) {
+  Widget build(BuildContext context, WidgetRef ref) {
     final location = GoRouterState.of(context).matchedLocation;
     final currentIndex = _tabs.indexOf(location).clamp(0, _tabs.length - 1);
 
+    // Count products expiring soon for the badge.
+    final expiringCount = ref.watch(productsProvider).maybeWhen(
+          data: (products) => products.where((p) => p.expiringSoon).length,
+          orElse: () => 0,
+        );
+
     return Scaffold(
       body: child,
       bottomNavigationBar: BottomNavigationBar(
         currentIndex: currentIndex,
         onTap: (index) => context.go(_tabs[index]),
-        items: const [
+        items: [
+          const BottomNavigationBarItem(
+            icon: Icon(Icons.home),
+            label: 'Главная',
+          ),
           BottomNavigationBarItem(
-              icon: Icon(Icons.home), label: 'Главная'),
-          BottomNavigationBarItem(
-              icon: Icon(Icons.kitchen), label: 'Продукты'),
-          BottomNavigationBarItem(
-              icon: Icon(Icons.calendar_month), label: 'Меню'),
-          BottomNavigationBarItem(
-              icon: Icon(Icons.menu_book), label: 'Рецепты'),
-          BottomNavigationBarItem(
-              icon: Icon(Icons.person), label: 'Профиль'),
+            icon: Badge(
+              isLabelVisible: expiringCount > 0,
+              label: Text('$expiringCount'),
+              child: const Icon(Icons.kitchen),
+            ),
+            label: 'Продукты',
+          ),
+          const BottomNavigationBarItem(
+            icon: Icon(Icons.calendar_month),
+            label: 'Меню',
+          ),
+          const BottomNavigationBarItem(
+            icon: Icon(Icons.menu_book),
+            label: 'Рецепты',
+          ),
+          const BottomNavigationBarItem(
+            icon: Icon(Icons.person),
+            label: 'Профиль',
+          ),
         ],
       ),
     );