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/lobbycache.ts

@@ -13,13 +13,18 @@ interface LobbySnapshot {
   // atGameLimit rides the snapshot so the lobby renders the "New Game" button in its last
   // known enabled/disabled state instantly (no flicker), then refreshes it in the background.
   atGameLimit: boolean;
+  // Which mode the snapshot belongs to (offline = device-local games, online = server games). The
+  // lobby renders it instantly only when it matches the current mode, so a mode flip never flashes —
+  // or lets the player open — the other mode's games before the background refresh replaces them.
+  offline: boolean;
 }
 
 let snapshot: LobbySnapshot | null = null;
 
-/** getLobby returns the last lobby lists, or null before the first load. */
-export function getLobby(): LobbySnapshot | null {
-  return snapshot;
+/** getLobby returns the last lobby lists for the given mode, or null before the first load or when
+ *  the cached snapshot belongs to the other mode (so the lobby cold-renders after a mode flip). */
+export function getLobby(offline: boolean): LobbySnapshot | null {
+  return snapshot && snapshot.offline === offline ? snapshot : null;
 }
 
 /** setLobby stores the latest lobby lists. */