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/ingredient/handler.go

@@ -0,0 +1,51 @@
+package ingredient
+
+import (
+	"encoding/json"
+	"log/slog"
+	"net/http"
+	"strconv"
+)
+
+// Handler handles ingredient HTTP requests.
+type Handler struct {
+	repo *Repository
+}
+
+// NewHandler creates a new Handler.
+func NewHandler(repo *Repository) *Handler {
+	return &Handler{repo: repo}
+}
+
+// Search handles GET /ingredients/search?q=&limit=10.
+func (h *Handler) Search(w http.ResponseWriter, r *http.Request) {
+	q := r.URL.Query().Get("q")
+	if q == "" {
+		w.Header().Set("Content-Type", "application/json")
+		_, _ = w.Write([]byte("[]"))
+		return
+	}
+
+	limit := 10
+	if s := r.URL.Query().Get("limit"); s != "" {
+		if n, err := strconv.Atoi(s); err == nil && n > 0 && n <= 50 {
+			limit = n
+		}
+	}
+
+	mappings, err := h.repo.Search(r.Context(), q, limit)
+	if err != nil {
+		slog.Error("search ingredients", "q", q, "err", err)
+		w.Header().Set("Content-Type", "application/json")
+		w.WriteHeader(http.StatusInternalServerError)
+		_, _ = w.Write([]byte(`{"error":"search failed"}`))
+		return
+	}
+
+	if mappings == nil {
+		mappings = []*IngredientMapping{}
+	}
+
+	w.Header().Set("Content-Type", "application/json")
+	_ = json.NewEncoder(w).Encode(mappings)
+}