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/screens/Lobby.svelte

@@ -17,6 +17,12 @@
   let games = $state<GameView[]>([]);
   let invitations = $state<Invitation[]>([]);
   let incoming = $state<AccountRef[]>([]);
+  // True when the player has reached the simultaneous quick-game cap: the "New Game" tab is
+  // disabled and a notice shows under the lists. It rides the games.list response (which the
+  // lobby refetches on entry and on every game event) and the cached snapshot, so it renders
+  // in its last known state instantly and refreshes in the background. Optimistic default
+  // (enabled) for the very first, uncached load; the backend gate is the authority.
+  let atGameLimit = $state(false);
 
   const guest = $derived(app.profile?.isGuest ?? true);
   // The lobby ⚙️ badge is the shared count: incoming friend requests plus an awaiting
@@ -25,7 +31,9 @@
 
   async function load() {
     try {
-      games = (await gateway.gamesList()).games;
+      const list = await gateway.gamesList();
+      games = list.games;
+      atGameLimit = list.atGameLimit;
       if (!guest) {
         [invitations, incoming] = await Promise.all([gateway.invitationsList(), gateway.friendsIncoming()]);
         // The ⚙️ badge counts incoming friend requests plus an awaiting feedback reply;
@@ -33,7 +41,7 @@
         app.notifications = incoming.length;
         void refreshFeedbackBadge();
       }
-      setLobby({ games, invitations, incoming });
+      setLobby({ games, invitations, incoming, atGameLimit });
       // Warm the cache for the ongoing games so opening one from the lobby is instant. The list
       // just loaded, so the connection is up; the call is non-blocking and re-running it on each
       // lobby refresh cheaply warms any newly appeared game (already-cached ones are skipped).
@@ -51,6 +59,7 @@
       games = cached.games;
       invitations = cached.invitations;
       incoming = cached.incoming;
+      atGameLimit = cached.atGameLimit;
     }
     void load();
   });
@@ -167,12 +176,12 @@
     revealedId = null;
     const prev = games;
     games = games.filter((g) => g.id !== id); // optimistic; the backend already filters it out
-    setLobby({ games, invitations, incoming });
+    setLobby({ games, invitations, incoming, atGameLimit });
     try {
       await gateway.hideGame(id);
     } catch (e) {
       games = prev;
-      setLobby({ games, invitations, incoming });
+      setLobby({ games, invitations, incoming, atGameLimit });
       handleError(e);
     }
   }
@@ -279,11 +288,15 @@
     {#if !games.length && !invitations.length}
       <p class="empty">{t('lobby.noActive')}</p>
     {/if}
+
+    {#if atGameLimit}
+      <p class="limit">{t('lobby.limitReached')}</p>
+    {/if}
   </div>
 
   {#snippet tabbar()}
     <TabBar>
-      <button class="tab" onclick={() => navigate('/new')}>
+      <button class="tab" disabled={atGameLimit} onclick={() => navigate('/new')}>
         <span class="sq">🎲</span><span class="lbl">{t('lobby.new')}</span>
       </button>
       <button class="tab" onclick={() => navigate('/stats')}>
@@ -316,6 +329,13 @@
     font-size: 0.9rem;
     margin: 0;
   }
+  /* A plain, low-emphasis line under the lists when the simultaneous-game cap is reached. */
+  .limit {
+    color: var(--text-muted);
+    font-size: 0.9rem;
+    margin: 0;
+    text-align: center;
+  }
   .invite {
     display: flex;
     align-items: center;