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/shared/models/ingredient_mapping.g.dart

@@ -0,0 +1,27 @@
+// GENERATED CODE - DO NOT MODIFY BY HAND
+
+part of 'ingredient_mapping.dart';
+
+// **************************************************************************
+// JsonSerializableGenerator
+// **************************************************************************
+
+IngredientMapping _$IngredientMappingFromJson(Map<String, dynamic> json) =>
+    IngredientMapping(
+      id: json['id'] as String,
+      canonicalName: json['canonical_name'] as String,
+      canonicalNameRu: json['canonical_name_ru'] as String?,
+      category: json['category'] as String?,
+      defaultUnit: json['default_unit'] as String?,
+      storageDays: (json['storage_days'] as num?)?.toInt(),
+    );
+
+Map<String, dynamic> _$IngredientMappingToJson(IngredientMapping instance) =>
+    <String, dynamic>{
+      'id': instance.id,
+      'canonical_name': instance.canonicalName,
+      'canonical_name_ru': instance.canonicalNameRu,
+      'category': instance.category,
+      'default_unit': instance.defaultUnit,
+      'storage_days': instance.storageDays,
+    };