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.ts

@@ -10,3 +10,14 @@ export const LOCAL_ID_PREFIX = 'local:';
 export function isLocalGameId(id: string): boolean {
   return id.startsWith(LOCAL_ID_PREFIX);
 }
+
+/** newLocalGameId mints a fresh, device-unique local game id (time + random suffix — no crypto API,
+ *  so it also works on the older engines the SPA still supports). */
+export function newLocalGameId(): string {
+  return `${LOCAL_ID_PREFIX}${Date.now().toString(36)}-${Math.random().toString(36).slice(2, 10)}`;
+}
+
+/** randomSeed returns a random 32-bit seed for a new local game's deterministic bag. */
+export function randomSeed(): bigint {
+  return BigInt(Math.floor(Math.random() * 0xffffffff));
+}