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/product.g.dart

@@ -0,0 +1,37 @@
+// GENERATED CODE - DO NOT MODIFY BY HAND
+
+part of 'product.dart';
+
+// **************************************************************************
+// JsonSerializableGenerator
+// **************************************************************************
+
+Product _$ProductFromJson(Map<String, dynamic> json) => Product(
+  id: json['id'] as String,
+  userId: json['user_id'] as String,
+  mappingId: json['mapping_id'] as String?,
+  name: json['name'] as String,
+  quantity: (json['quantity'] as num).toDouble(),
+  unit: json['unit'] as String,
+  category: json['category'] as String?,
+  storageDays: (json['storage_days'] as num).toInt(),
+  addedAt: DateTime.parse(json['added_at'] as String),
+  expiresAt: DateTime.parse(json['expires_at'] as String),
+  daysLeft: (json['days_left'] as num).toInt(),
+  expiringSoon: json['expiring_soon'] as bool,
+);
+
+Map<String, dynamic> _$ProductToJson(Product instance) => <String, dynamic>{
+  'id': instance.id,
+  'user_id': instance.userId,
+  'mapping_id': instance.mappingId,
+  'name': instance.name,
+  'quantity': instance.quantity,
+  'unit': instance.unit,
+  'category': instance.category,
+  'storage_days': instance.storageDays,
+  'added_at': instance.addedAt.toIso8601String(),
+  'expires_at': instance.expiresAt.toIso8601String(),
+  'days_left': instance.daysLeft,
+  'expiring_soon': instance.expiringSoon,
+};