fix(offline): zero tile weights on cold boot + wrong-mode game in the lobby

Two pre-existing offline bugs, both exposed once offline mode became usable (cold boot +
toggling), owner-reported on the contour.

Bug 1 -- offline tiles render weight 0. The rack/board read tile values from the
lib/alphabet cache, populated only by the online wire codec (server-sent alphabet) or the
mock (so the e2e masked it). A local game never goes through the codec, so on a cold
offline boot with no prior online session the cache was empty and every value read 0
(scores stayed correct -- they come from the offline ruleset). Fix: the local source
seeds lib/alphabet from the static offline ruleset (letters + values) when it builds a
game view.

Bug 2 -- the lobby showed (and could open) the other mode's game after a toggle. Two
causes: (a) the lobby cache was not mode-tagged, so getLobby() instant-rendered the last
snapshot regardless of mode; (b) load() wrote the module list after an await with no
generation guard, so a slow online gamesList() finishing after a fast offline list() (or
vice versa) left the wrong mode's games on screen. Fix: tag the snapshot with offline and
gate getLobby() on it; add a load-sequence guard so only the latest load() writes.

- localgame/source.ts: ensureAlphabet from the ruleset in gameView (+ unit test).
- lobbycache.ts: LobbySnapshot.offline + getLobby(offline) mode check (+ tests).
- Lobby.svelte: setLobby tags the mode; load() carries a generation guard.

check 0 / unit 485 / e2e 198 / app entry 113.8/114.

ui/src/lib/localgame/source.test.ts

@@ -13,6 +13,7 @@ vi.mock('../dict', () => ({
 
 import { LocalSource, isLocalGameId } from './source';
 import type { Seat } from './serialize';
+import { hasAlphabet, alphabetValues } from '../alphabet';
 
 const seats: Seat[] = [
   { kind: 'human', name: 'You' },
@@ -42,6 +43,18 @@ describe('LocalSource', () => {
     expect(st.game.toMove).toBe(0);
   });
 
+  it('seeds the per-variant alphabet from the ruleset, so offline tiles show real weights not zeros', async () => {
+    // Offline there is no server to send the alphabet table the rack/board render from; opening a
+    // local game must seed it from the static ruleset. Without this a cold offline boot draws zeros.
+    const src = await newSource('local:gAlpha', 42n);
+    await src.gameState('local:gAlpha');
+    expect(hasAlphabet('scrabble_en')).toBe(true);
+    const values = alphabetValues('scrabble_en');
+    expect(values.length).toBe(26);
+    expect(values[0]).toBe(1); // A = 1 (pinned to rules.go / ruleset.ts), not 0
+    expect(values.every((v) => v > 0)).toBe(true);
+  });
+
   it('replies to a human pass with a synchronous robot move, delivered via the event', async () => {
     const src = await newSource('local:g2', 999n);
     const events: PushEvent[] = [];