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/UI_DESIGN.md

@@ -240,6 +240,13 @@ opponent's-turn change is silent. Each card's blink is keyed by game id, so over
 events animate in isolation, and the newest bottom toast cancels the previous one and replays
 its entrance (`components/Toast.svelte`, re-keyed on a per-message sequence).
 
+**Simultaneous-game cap.** When the player is at the active-quick-game cap (`games.list`
+`at_game_limit`), the lobby's **New Game** tab is **disabled** (greyed via the shared
+`.tab:disabled` opacity) and a plain, low-emphasis line — muted, centred, no accent — sits
+under the lists with the localized "limit reached" notice. Both follow the flag carried in the
+cached lobby snapshot, so they render in their last-known state on entry (the button stays
+enabled on the first, uncached load) and flip in place when an event refreshes the lobby.
+
 ## Social, account & history surfaces
 
 - **Settings hub** (`screens/SettingsHub.svelte`, the lobby ⚙️ tab): one nav bar + a bottom