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/lib/localgame/id.test.ts

@@ -0,0 +1,24 @@
+import { describe, it, expect } from 'vitest';
+import { LOCAL_ID_PREFIX, isLocalGameId, newLocalGameId, randomSeed } from './id';
+
+describe('local game id helpers', () => {
+  it('recognises local ids by prefix', () => {
+    expect(isLocalGameId(LOCAL_ID_PREFIX + 'x')).toBe(true);
+    expect(isLocalGameId('deadbeef')).toBe(false);
+  });
+
+  it('mints unique local ids', () => {
+    const a = newLocalGameId();
+    const b = newLocalGameId();
+    expect(isLocalGameId(a)).toBe(true);
+    expect(a).not.toBe(b);
+  });
+
+  it('produces a bigint seed in the 32-bit range', () => {
+    for (let i = 0; i < 50; i++) {
+      const s = randomSeed();
+      expect(typeof s).toBe('bigint');
+      expect(s >= 0n && s <= 0xffffffffn).toBe(true);
+    }
+  });
+});