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>

backend/internal/recommendation/handler.go

@@ -23,6 +23,11 @@ type UserLoader interface {
 	GetByID(ctx context.Context, id string) (*user.User, error)
 }
 
+// ProductLister returns a human-readable list of user's products for the AI prompt.
+type ProductLister interface {
+	ListForPrompt(ctx context.Context, userID string) ([]string, error)
+}
+
 // userPreferences is the shape of user.Preferences JSONB.
 type userPreferences struct {
 	Cuisines     []string `json:"cuisines"`
@@ -31,17 +36,19 @@ type userPreferences struct {
 
 // Handler handles GET /recommendations.
 type Handler struct {
-	gemini     *gemini.Client
-	pexels     PhotoSearcher
-	userLoader UserLoader
+	gemini        *gemini.Client
+	pexels        PhotoSearcher
+	userLoader    UserLoader
+	productLister ProductLister
 }
 
 // NewHandler creates a new Handler.
-func NewHandler(geminiClient *gemini.Client, pexels PhotoSearcher, userLoader UserLoader) *Handler {
+func NewHandler(geminiClient *gemini.Client, pexels PhotoSearcher, userLoader UserLoader, productLister ProductLister) *Handler {
 	return &Handler{
-		gemini:     geminiClient,
-		pexels:     pexels,
-		userLoader: userLoader,
+		gemini:        geminiClient,
+		pexels:        pexels,
+		userLoader:    userLoader,
+		productLister: productLister,
 	}
 }
 
@@ -69,6 +76,13 @@ func (h *Handler) GetRecommendations(w http.ResponseWriter, r *http.Request) {
 
 	req := buildRecipeRequest(u, count)
 
+	// Attach available products to personalise the prompt.
+	if products, err := h.productLister.ListForPrompt(r.Context(), userID); err == nil {
+		req.AvailableProducts = products
+	} else {
+		slog.Warn("load products for recommendations", "user_id", userID, "err", err)
+	}
+
 	recipes, err := h.gemini.GenerateRecipes(r.Context(), req)
 	if err != nil {
 		slog.Error("generate recipes", "user_id", userID, "err", err)