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/FUNCTIONAL.md

@@ -256,6 +256,18 @@ the same occasional move against its plan that fades out by the endgame), and ch
 add-friend are off. AI games are **practice** — they never count toward a player's
 statistics.
 
+### Offline mode
+An installed web PWA signed in with a confirmed email can switch to a deliberate **offline mode**
+(Settings → Play mode). Offline, the app never touches the network: the header turns blue with an
+*Offline* chip, the lobby lists only the games stored on the device, and online-only surfaces are
+disabled or hidden (the Stats tab; the *with friends* and *random opponent* options in New Game).
+Only **vs_ai** games are playable — New Game creates a device-local game against the robot, which
+plays entirely in the browser with no backend. Local games are kept on the device, visible only in
+offline mode, and never sync to the account. So a game can be created and played with no connection,
+the app quietly preloads the dictionaries for the player's enabled variants while still online, and
+(once installed) launches from a precached shell even with no network. The mode is device-scoped and
+sticky across launches.
+
 ### Social: friends, block, chat, nudge
 Become friends in two ways: redeem a **one-time code** the other player issues (six
 digits, valid for twelve hours), or send a **request to someone you have played