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.dart

@@ -0,0 +1,46 @@
+import 'package:json_annotation/json_annotation.dart';
+
+part 'product.g.dart';
+
+@JsonSerializable()
+class Product {
+  final String id;
+  @JsonKey(name: 'user_id')
+  final String userId;
+  @JsonKey(name: 'mapping_id')
+  final String? mappingId;
+  final String name;
+  final double quantity;
+  final String unit;
+  final String? category;
+  @JsonKey(name: 'storage_days')
+  final int storageDays;
+  @JsonKey(name: 'added_at')
+  final DateTime addedAt;
+  @JsonKey(name: 'expires_at')
+  final DateTime expiresAt;
+  @JsonKey(name: 'days_left')
+  final int daysLeft;
+  @JsonKey(name: 'expiring_soon')
+  final bool expiringSoon;
+
+  const Product({
+    required this.id,
+    required this.userId,
+    this.mappingId,
+    required this.name,
+    required this.quantity,
+    required this.unit,
+    this.category,
+    required this.storageDays,
+    required this.addedAt,
+    required this.expiresAt,
+    required this.daysLeft,
+    required this.expiringSoon,
+  });
+
+  factory Product.fromJson(Map<String, dynamic> json) =>
+      _$ProductFromJson(json);
+
+  Map<String, dynamic> toJson() => _$ProductToJson(this);
+}