Stage 13: alphabet on the wire (UI alphabet-agnostic, TODO-4)

Live play now exchanges per-variant alphabet indices instead of concrete
letters (rack out; submit-play, evaluate, exchange, word-check in). The client
caches each variant's (index, letter, value) table behind
StateRequest.include_alphabet and renders the rack and blank chooser from it,
dropping the hardcoded value/alphabet tables. History, the durable journal and
GCG stay decoded concrete characters (ARCHITECTURE §9.1, unchanged).

- pkg/fbs: new AlphabetEntry + PlayTile; StateView.rack -> [ubyte] + alphabet;
  StateRequest.include_alphabet; SubmitPlay/Eval tiles -> [PlayTile];
  Exchange tiles + CheckWord word -> [ubyte] (committed Go + TS regenerated).
- engine: AlphabetTable + a cached per-variant codec (LetterForIndex/EncodeRack/
  DecodeTiles/DecodeWord) + BlankIndex sentinel; Go parity test.
- backend server edge maps index<->letter (new thin game.Service.GameVariant);
  game.Service domain methods, engine.Game and the robot keep one letter-based
  play path. The gateway forwards indices verbatim (no alphabet table).
- ui: lib/alphabet.ts in-memory cache; codec encodes/decodes indices; premiums.ts
  is geometry-only; the mock seeds a fixture table; the UI normalises display to
  upper case (codec + cache), leaving placement/board/checkword unchanged.

Parity moved to the Go engine.AlphabetTable test; premiums.ts loses its value
tables. Discharges TODO-4.

backend/internal/inttest/game_test.go

@@ -428,6 +428,26 @@ func TestHintPolicy(t *testing.T) {
 	}
 }
 
+// TestGameVariant covers the edge's lightweight variant lookup (Stage 13): it returns the
+// created game's variant and ErrNotFound for an unknown id.
+func TestGameVariant(t *testing.T) {
+	ctx := context.Background()
+	svc := newGameService()
+	seats := []uuid.UUID{provisionAccount(t), provisionAccount(t)}
+	g, err := svc.Create(ctx, game.CreateParams{
+		Variant: engine.VariantEnglish, Seats: seats, TurnTimeout: time.Hour, Seed: 1,
+	})
+	if err != nil {
+		t.Fatalf("create: %v", err)
+	}
+	if v, err := svc.GameVariant(ctx, g.ID); err != nil || v != engine.VariantEnglish {
+		t.Fatalf("GameVariant = %v, %v; want english, nil", v, err)
+	}
+	if _, err := svc.GameVariant(ctx, uuid.New()); !errors.Is(err, game.ErrNotFound) {
+		t.Errorf("GameVariant(unknown) = %v, want ErrNotFound", err)
+	}
+}
+
 // TestCheckWordAndComplaint covers the word-check tool and complaint capture.
 func TestCheckWordAndComplaint(t *testing.T) {
 	ctx := context.Background()