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/gemini/recipe.go

@@ -14,11 +14,12 @@ type RecipeGenerator interface {
 
 // RecipeRequest contains parameters for recipe generation.
 type RecipeRequest struct {
-	UserGoal      string   // "weight_loss" | "maintain" | "gain"
-	DailyCalories int
-	Restrictions  []string // e.g. ["gluten_free", "vegetarian"]
-	CuisinePrefs  []string // e.g. ["russian", "asian"]
-	Count         int
+	UserGoal          string   // "weight_loss" | "maintain" | "gain"
+	DailyCalories     int
+	Restrictions      []string // e.g. ["gluten_free", "vegetarian"]
+	CuisinePrefs      []string // e.g. ["russian", "asian"]
+	Count             int
+	AvailableProducts []string // human-readable list of products in user's pantry
 }
 
 // Recipe is a recipe returned by Gemini.
@@ -134,6 +135,13 @@ func buildRecipePrompt(req RecipeRequest) string {
 		perMealCalories = 600
 	}
 
+	productsSection := ""
+	if len(req.AvailableProducts) > 0 {
+		productsSection = "\nДоступные продукты (приоритет — скоро истекают ⚠):\n" +
+			strings.Join(req.AvailableProducts, "\n") +
+			"\nПредпочтительно использовать эти продукты в рецептах.\n"
+	}
+
 	return fmt.Sprintf(`Ты — диетолог-повар. Предложи %d рецептов на русском языке.
 
 Профиль пользователя:
@@ -141,7 +149,7 @@ func buildRecipePrompt(req RecipeRequest) string {
 - Дневная норма калорий: %d ккал
 - Ограничения: %s
 - Предпочтения: %s
-
+%s
 Требования к каждому рецепту:
 - Калорийность на порцию: не более %d ккал
 - Время приготовления: до 60 минут
@@ -165,7 +173,7 @@ func buildRecipePrompt(req RecipeRequest) string {
   "nutrition_per_serving": {
     "calories": 420, "protein_g": 48, "fat_g": 12, "carbs_g": 18
   }
-}]`, count, goal, req.DailyCalories, restrictions, cuisines, perMealCalories)
+}]`, count, goal, req.DailyCalories, restrictions, cuisines, productsSection, perMealCalories)
 }
 
 func parseRecipesJSON(text string) ([]Recipe, error) {