feat: move supported languages to DB table, expose via GET /languages

- migration 013: create languages table (code PK, native_name, english_name,
  is_active, sort_order) with all 12 existing languages seeded
- locale: add Language struct, Languages []Language, LoadFromDB() — queries
  languages table at startup and populates both Supported map and Languages
  slice; existing Parse/FromContext/FromRequest unchanged
- main.go: call locale.LoadFromDB after pool is ready
- gemini/recipe.go: remove hardcoded langNames map, use locale.Languages
  linear lookup for English name in prompt
- language/handler.go: new package with GET /languages handler returning
  active languages list (no auth required)
- server.go: register GET /languages as public route
- Flutter: add LanguageRepository + languageRepositoryProvider that fetches
  /languages from backend
- language_provider.dart: replace const supportedLanguages map with
  supportedLanguagesProvider (FutureProvider) backed by LanguageRepository
- profile_provider.dart: remove supportedLanguages.containsKey validation —
  backend is source of truth; sync any non-empty language from preferences
- profile_screen.dart: use supportedLanguagesProvider for display name and
  dropdown (async with loading/error states)

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

backend/internal/locale/locale.go

@@ -2,8 +2,11 @@ package locale
 
 import (
 	"context"
+	"fmt"
 	"net/http"
 	"strings"
+
+	"github.com/jackc/pgx/v5/pgxpool"
 )
 
 // Default is the fallback language when no supported language is detected.
@@ -11,19 +14,49 @@ const Default = "en"
 
 // Supported is the set of language codes the application currently handles.
 // Keys are ISO 639-1 two-letter codes (lower-case).
+// Populated by LoadFromDB at server startup.
 var Supported = map[string]bool{
 	"en": true,
 	"ru": true,
-	"es": true,
-	"de": true,
-	"fr": true,
-	"it": true,
-	"pt": true,
-	"zh": true,
-	"ja": true,
-	"ko": true,
-	"ar": true,
-	"hi": true,
+}
+
+// Language is a supported language record loaded from the DB.
+type Language struct {
+	Code        string
+	NativeName  string
+	EnglishName string
+}
+
+// Languages is the ordered list of active languages.
+// Populated by LoadFromDB at server startup.
+var Languages []Language
+
+// LoadFromDB queries the languages table and updates both Supported and Languages.
+// Must be called once at startup before the server begins accepting requests.
+func LoadFromDB(ctx context.Context, pool *pgxpool.Pool) error {
+	rows, err := pool.Query(ctx,
+		`SELECT code, native_name, english_name FROM languages WHERE is_active ORDER BY sort_order`)
+	if err != nil {
+		return fmt.Errorf("load languages from db: %w", err)
+	}
+	defer rows.Close()
+
+	newSupported := map[string]bool{}
+	var newLanguages []Language
+	for rows.Next() {
+		var l Language
+		if err := rows.Scan(&l.Code, &l.NativeName, &l.EnglishName); err != nil {
+			return err
+		}
+		newSupported[l.Code] = true
+		newLanguages = append(newLanguages, l)
+	}
+	if err := rows.Err(); err != nil {
+		return err
+	}
+	Supported = newSupported
+	Languages = newLanguages
+	return nil
 }
 
 type contextKey struct{}