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/e2e/gamelimit.spec.ts

@@ -0,0 +1,31 @@
+import { expect, test } from './fixtures';
+
+// The simultaneous quick-game cap. When the backend reports the player is at the limit
+// (games.list at_game_limit), the lobby disables the "New Game" tab and shows a plain,
+// low-emphasis notice under the lists; when it clears, the button re-enables and the
+// notice goes. Driven by the mock transport's __mock.setGameLimit seam (no backend), which
+// also nudges the lobby to re-fetch (the lobby refreshes on any live event).
+
+test('lobby: New Game disables and a notice shows at the simultaneous-game limit', async ({ page }) => {
+  await page.goto('/');
+  await page.getByRole('button', { name: /guest/i }).click();
+
+  // Below the limit: the New Game tab is enabled and no notice is shown.
+  const newGame = page.getByRole('button', { name: /New/ });
+  await expect(newGame).toBeEnabled();
+  await expect(page.getByText(/reached the simultaneous games limit/i)).toHaveCount(0);
+
+  // Reach the limit: the button greys out (disabled) and the notice appears under the lists.
+  await page.evaluate(() =>
+    (window as unknown as { __mock: { setGameLimit(v: boolean): void } }).__mock.setGameLimit(true),
+  );
+  await expect(newGame).toBeDisabled();
+  await expect(page.getByText(/reached the simultaneous games limit/i)).toBeVisible();
+
+  // Drop back below the limit (a game finished): the button re-enables and the notice clears.
+  await page.evaluate(() =>
+    (window as unknown as { __mock: { setGameLimit(v: boolean): void } }).__mock.setGameLimit(false),
+  );
+  await expect(newGame).toBeEnabled();
+  await expect(page.getByText(/reached the simultaneous games limit/i)).toHaveCount(0);
+});