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

docs/FUNCTIONAL.md

@@ -110,6 +110,15 @@ is shareable as a Telegram deep link that opens it directly): the inviter choose
 settings and the game starts once every invitee has accepted — any decline cancels it, and an unanswered invitation
 expires after seven days.
 
+**Simultaneous-game cap.** A player may hold at most **10 active quick games** at once —
+counting both in-progress and still-searching auto-match/AI games, but **not** friend games
+created by invitation. At the cap the **New Game** button is disabled (greyed) and a plain,
+low-emphasis line under the lists reads *"You've reached the simultaneous games limit."*; both
+clear automatically once an active game finishes and the count drops below ten. The cap blocks
+**starting** any game (a quick game or a friend invitation, which share the New Game entry), but
+**accepting an incoming invitation is never blocked** — so friend games are capped from the other
+end (you cannot initiate one while at the cap) while you can always join a game you are invited to.
+
 ### Playing a game
 Place tiles, pass, exchange, or resign. Pass and exchange share one control —
 choosing no tiles passes the turn, choosing tiles exchanges them. Tiles are laid