feat(lobby): cap simultaneous quick games at 10

Limit a player to 10 active quick games (auto-match + AI); friend games created
by invitation are not counted. At the cap the backend refuses both new-game
entry points — quick enqueue and invitation creation — with 409
game_limit_reached, while accepting an incoming invitation stays allowed, so
friend games are capped from the other end. The lobby disables "New Game" and
shows a low-emphasis notice, driven by a new at_game_limit flag on games.list
(no per-event payload: a turn change does not move the count, and the lobby
already re-fetches games.list on entry and every game event).

- game.MaxActiveQuickGames + Store/Service.CountActiveQuickGames (active/open
  seats, no game_invitations row; hidden games still count -> dedicated count)
- Server.ensureUnderGameLimit gating handleEnqueue + handleCreateInvitation;
  game.ErrGameLimitReached -> 409 game_limit_reached
- FB GameList.at_game_limit (regenerated Go + TS) through the gateway transcode
  and UI codec; gameListDTO + lobbycache snapshot + Lobby.svelte + i18n
- tests: integration count rule + HTTP gate + accept bypass; server error map;
  gateway transcode round-trip; UI codec + lobbycache unit; e2e gamelimit
- docs: PRERELEASE (GL), FUNCTIONAL(+ru), ARCHITECTURE 8, UI_DESIGN, backend README

gateway/internal/transcode/encode.go

@@ -352,6 +352,7 @@ func encodeGameList(r backendclient.GameListResp) []byte {
 	games := b.EndVector(len(gameOffs))
 	fb.GameListStart(b)
 	fb.GameListAddGames(b, games)
+	fb.GameListAddAtGameLimit(b, r.AtGameLimit)
 	b.Finish(fb.GameListEnd(b))
 	return b.FinishedBytes()
 }

gateway/internal/transcode/transcode_test.go

@@ -221,7 +221,7 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 		if r.URL.Path != "/api/v1/user/games" {
 			t.Errorf("unexpected path %q", r.URL.Path)
 		}
-		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":0,"last_activity_unix":1717000000,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}]}`))
+		_, _ = w.Write([]byte(`{"games":[{"id":"g-1","variant":"scrabble_en","status":"active","players":2,"to_move":0,"last_activity_unix":1717000000,"seats":[{"seat":0,"account_id":"u-9","display_name":"You","score":10},{"seat":1,"account_id":"a-1","display_name":"Ann","score":7}]}],"at_game_limit":true}`))
 	})
 	defer cleanup()
 
@@ -248,6 +248,9 @@ func TestGamesListRoundTripDecodesSeatNames(t *testing.T) {
 	if string(seat.DisplayName()) != "Ann" {
 		t.Errorf("seat display name = %q, want Ann", seat.DisplayName())
 	}
+	if !gl.AtGameLimit() {
+		t.Error("at_game_limit = false, want true (the backend reported the cap)")
+	}
 }
 
 func TestPassRoundTrip(t *testing.T) {