feat: food search sheet with FTS+trgm, dish/recent endpoints, multilingual aliases

Backend:
- GET /dishes/search — hybrid FTS (english + simple) + trgm + ILIKE search
- GET /diary/recent — recently used dishes and products for the current user
- product search upgraded: FTS on canonical_name and product_aliases, ranked by GREATEST(ts_rank, similarity)
- importoff: collect product_name_ru/de/fr/... as product_aliases for multilingual search (e.g. "сникерс" → "Snickers")
- migrations: FTS + trgm indexes merged into 001_initial_schema.sql (002 removed)

Flutter:
- FoodSearchSheet: debounced search field, recently-used section, product/dish results, scan-photo and barcode chips
- DishPortionSheet: quick ½/1/1½/2 buttons + custom input
- + button in meal card now opens FoodSearchSheet instead of going directly to AI scan
- 7 new l10n keys across all 12 languages

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/internal/domain/dish/entity.go

@@ -59,6 +59,14 @@ type RecipeStep struct {
 	ImageURL     *string `json:"image_url"`
 }
 
+// DishSearchResult is a lightweight dish returned by the search endpoint.
+type DishSearchResult struct {
+	ID       string   `json:"id"`
+	Name     string   `json:"name"`
+	ImageURL *string  `json:"image_url,omitempty"`
+	AvgRating float64 `json:"avg_rating"`
+}
+
 // CreateRequest is the body used to create a new dish + recipe at once.
 // Used when saving a Gemini-generated recommendation.
 type CreateRequest struct {

backend/internal/domain/dish/handler.go

@@ -4,6 +4,7 @@ import (
 	"encoding/json"
 	"log/slog"
 	"net/http"
+	"strconv"
 
 	"github.com/go-chi/chi/v5"
 )
@@ -18,6 +19,31 @@ func NewHandler(repo *Repository) *Handler {
 	return &Handler{repo: repo}
 }
 
+// Search handles GET /dishes/search?q=<query>&limit=<n>
+func (h *Handler) Search(w http.ResponseWriter, r *http.Request) {
+	query := r.URL.Query().Get("q")
+	if query == "" {
+		writeJSON(w, http.StatusOK, []*DishSearchResult{})
+		return
+	}
+	limit := 10
+	if limitStr := r.URL.Query().Get("limit"); limitStr != "" {
+		if parsed, parseError := strconv.Atoi(limitStr); parseError == nil && parsed > 0 && parsed <= 50 {
+			limit = parsed
+		}
+	}
+	results, searchError := h.repo.Search(r.Context(), query, limit)
+	if searchError != nil {
+		slog.Error("search dishes", "err", searchError)
+		writeError(w, http.StatusInternalServerError, "failed to search dishes")
+		return
+	}
+	if results == nil {
+		results = []*DishSearchResult{}
+	}
+	writeJSON(w, http.StatusOK, results)
+}
+
 // List handles GET /dishes — returns all dishes (no recipe variants).
 func (h *Handler) List(w http.ResponseWriter, r *http.Request) {
 	dishes, err := h.repo.List(r.Context())

backend/internal/domain/dish/repository.go

@@ -98,6 +98,57 @@ func (r *Repository) List(ctx context.Context) ([]*Dish, error) {
 	return dishes, nil
 }
 
+// Search finds dishes matching the query string using FTS + trigram similarity.
+// Text is resolved for the language in ctx (English fallback).
+func (r *Repository) Search(ctx context.Context, query string, limit int) ([]*DishSearchResult, error) {
+	if limit <= 0 || limit > 50 {
+		limit = 10
+	}
+	lang := locale.FromContext(ctx)
+
+	const searchQuery = `
+		SELECT d.id,
+			COALESCE(dt.name, d.name) AS name,
+			d.image_url,
+			d.avg_rating,
+			GREATEST(
+				ts_rank(to_tsvector('english', d.name), plainto_tsquery('english', $1)),
+				ts_rank(to_tsvector('simple',  COALESCE(dt.name, '')), plainto_tsquery('simple', $1)),
+				similarity(COALESCE(dt.name, d.name), $1)
+			) AS rank
+		FROM dishes d
+		LEFT JOIN dish_translations dt ON dt.dish_id = d.id AND dt.lang = $3
+		WHERE (
+			to_tsvector('english', d.name) @@ plainto_tsquery('english', $1)
+			OR to_tsvector('simple', COALESCE(dt.name, '')) @@ plainto_tsquery('simple', $1)
+			OR d.name  ILIKE '%' || $1 || '%'
+			OR dt.name ILIKE '%' || $1 || '%'
+			OR similarity(COALESCE(dt.name, d.name), $1) > 0.3
+		)
+		ORDER BY rank DESC
+		LIMIT $2`
+
+	rows, queryError := r.pool.Query(ctx, searchQuery, query, limit, lang)
+	if queryError != nil {
+		return nil, fmt.Errorf("search dishes: %w", queryError)
+	}
+	defer rows.Close()
+
+	var results []*DishSearchResult
+	for rows.Next() {
+		var result DishSearchResult
+		var rank float64
+		if scanError := rows.Scan(&result.ID, &result.Name, &result.ImageURL, &result.AvgRating, &rank); scanError != nil {
+			return nil, fmt.Errorf("scan dish search result: %w", scanError)
+		}
+		results = append(results, &result)
+	}
+	if err := rows.Err(); err != nil {
+		return nil, err
+	}
+	return results, nil
+}
+
 // FindOrCreate returns the dish ID and whether it was newly created.
 // Looks up by case-insensitive name match; creates a minimal dish row if not found.
 func (r *Repository) FindOrCreate(ctx context.Context, name string) (id string, created bool, err error) {