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

ui/src/lib/mock/client.ts

@@ -98,6 +98,8 @@ export class MockGateway implements GatewayClient {
   private feedbackReplyUnread = false;
   // The most recently opened auto-match game still awaiting an opponent, for the e2e join hook.
   private openGameId: string | null = null;
+  // gameLimit forces the lobby's at_game_limit flag for the e2e (window.__mock.setGameLimit).
+  private gameLimit = false;
   private friends: AccountRef[] = MOCK_FRIENDS.map((f) => ({ ...f }));
   private incoming: AccountRef[] = MOCK_INCOMING.map((f) => ({ ...f }));
   private outgoing: AccountRef[] = [];
@@ -152,7 +154,10 @@ export class MockGateway implements GatewayClient {
     return { blocked: false, permanent: false, until: '', reason: '' };
   }
   async gamesList(): Promise<GameList> {
-    return { games: [...this.games.values()].map((g) => structuredClone(g.view)) };
+    return {
+      games: [...this.games.values()].map((g) => structuredClone(g.view)),
+      atGameLimit: this.gameLimit,
+    };
   }
 
   // --- lobby ---
@@ -257,6 +262,15 @@ export class MockGateway implements GatewayClient {
     if (this.openGameId) this.seatOpponent(this.openGameId);
   }
 
+  // setGameLimit forces the lobby's at_game_limit flag (the e2e hook
+  // window.__mock.setGameLimit), then nudges the lobby to re-fetch games.list so the
+  // "New Game" button and the notice update in place. The lobby refetches on any
+  // non-heartbeat event; an unrecognised notify sub triggers only that refetch.
+  setGameLimit(v: boolean): void {
+    this.gameLimit = v;
+    this.emit({ kind: 'notify', sub: 'game_limit' });
+  }
+
   async lobbyPoll(): Promise<MatchResult> {
     if (this.pendingMatch) {
       const g = this.games.get(this.pendingMatch);