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

backend/internal/game/service.go

@@ -1178,6 +1178,14 @@ func (svc *Service) ListForAccount(ctx context.Context, accountID uuid.UUID) ([]
 	return svc.store.ListGamesForAccount(ctx, accountID)
 }
 
+// CountActiveQuickGames reports how many in-progress quick games the account holds —
+// the count the simultaneous-game limit (MaxActiveQuickGames) is checked against. It
+// counts active and still-open quick games (including honest-AI ones) and excludes
+// friend games created by invitation and finished games. See Store.CountActiveQuickGames.
+func (svc *Service) CountActiveQuickGames(ctx context.Context, accountID uuid.UUID) (int, error) {
+	return svc.store.CountActiveQuickGames(ctx, accountID)
+}
+
 // HideGame hides a finished game from accountID's own lobby (it stays visible to the other
 // players); it is irreversible by design. Only a player of a finished game may hide it
 // (ErrNotAPlayer / ErrGameActive otherwise); hiding an already-hidden game is a no-op.