feat(offline): offline lobby lists + creates local vs_ai games

In offline mode the lobby now shows only the device-local games and its
New-vs-AI entry creates one through the in-browser engine — the visible
payoff of the offline mode.

- LocalSource.list() reconstructs a lobby GameView per stored local game by
  replay, exposed through the lazy gamesource proxy; unit-tested via an
  in-memory store.
- Lobby.load() branches on offlineMode: lists local games and skips every
  gateway call (no online games/invitations/incoming); the Stats tab is
  disabled offline.
- NewGame offline: find() creates a device-local vs_ai game via
  LocalSource.create using the profile's advertised dict version + a local
  seed; the friends flow and the random-opponent option are hidden, and the
  variant picker / Start are enabled offline (were gated on connection).
- id.ts: newLocalGameId + randomSeed (tested).

Docs: ARCHITECTURE + FUNCTIONAL(+ru) offline-mode section.

Deferred to fast-follow: the Settings Friends/Profile/Feedback affordance
gating, the flip-to-offline readiness wait, the offline mock e2e (needs
mock-dawg support), and the local-hint UI. The offline flow is verified on
the test contour — the mock e2e cannot enter offline mode (the toggle is
gated to an installed PWA).

ui/src/screens/Lobby.svelte

@@ -13,7 +13,8 @@
   import { badgeKind } from '../lib/unread';
   import { getLobby, setLobby } from '../lib/lobbycache';
   import { preloadGames } from '../lib/preload';
-  import { kickDictPreload } from '../lib/offline.svelte';
+  import { kickDictPreload, offlineMode } from '../lib/offline.svelte';
+  import { localSource } from '../lib/gamesource';
   import { gamePhase, groupGames, orderedSeats, scoreStanding, shouldBlink, type LobbyPhase } from '../lib/lobbysort';
   import type { AccountRef, GameView, Invitation } from '../lib/model';
   import { VARIANT_FLAG, VARIANT_RULES } from '../lib/variants';
@@ -34,6 +35,19 @@
   const settingsBadge = $derived(app.notifications + (app.feedbackReplyUnread ? 1 : 0));
 
   async function load() {
+    // Deliberate offline mode: never touch the network. The lobby shows only the device-local
+    // vs_ai games (reconstructed from the store) plus the New-vs-AI entry; there are no online
+    // games, invitations or incoming requests to fetch.
+    if (offlineMode.active) {
+      games = await localSource.list();
+      invitations = [];
+      incoming = [];
+      atGameLimit = false;
+      app.notifications = 0;
+      setLobby({ games, invitations, incoming, atGameLimit });
+      app.lobbyReady = true;
+      return;
+    }
     try {
       const list = await gateway.gamesList();
       games = list.games;
@@ -341,7 +355,7 @@
       <button class="tab" disabled={atGameLimit} onclick={() => navigate('/new')}>
         <span class="sq" data-coach="lobby-new">🎲</span><span class="lbl">{t('lobby.new')}</span>
       </button>
-      <button class="tab" onclick={() => navigate('/stats')}>
+      <button class="tab" disabled={offlineMode.active} onclick={() => navigate('/stats')}>
         <span class="sq" data-coach="lobby-stats">✏️</span><span class="lbl">{t('lobby.stats')}</span>
       </button>
       <button class="tab" onclick={() => navigate('/settings')}>