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).

docs/ARCHITECTURE.md

@@ -1248,8 +1248,12 @@ and the Connect stream and runtime API POSTs are never precached nor intercepted
 never served stale. This satisfies Chromium's installability requirement (a registered SW, needed
 for install on Android) and powers the opt-in **offline mode** (in progress): a deliberate, device-scoped Settings
 toggle — distinct from the transient gateway-reachability signal — that tints the header blue with
-an *Offline* chip and confines play to on-device `vs_ai` games. To have data ready before the
-switch, the **Profile advertises the current dictionary version per variant** (`dict_versions`,
+an *Offline* chip and confines play to on-device `vs_ai` games. The **offline lobby lists only those
+device-local games** (reconstructed by replaying the IndexedDB move journal) and its New-vs-AI entry
+creates one through the in-browser engine — the same game screen then drives it, the robot replying
+locally; online-only affordances (the Stats tab, the friend/random options in New Game) are disabled
+or hidden. To have data ready before the switch, the **Profile advertises the current dictionary
+version per variant** (`dict_versions`,
 filled from the registry on the existing cold-start profile request — no extra round-trip), and an
 eligible installed PWA (standalone web + confirmed email) **background-preloads** those dictionaries
 — on lobby entry and on a variant-preference change — through the same three-tier loader, retried