fix(offline): route word-check through the game source; reload lobby on offline flip

Two offline bugs found on the contour:
- The word-check screen (CheckScreen) called gateway.gameState/checkWord
  directly, so in an offline (local) game it hit the network and errored
  ("something went wrong"). Route both through gameSource(id) — the local
  source answers from the device dawg. The complaint control (online-only,
  no offline backend) is hidden for a local game.
- The lobby did not react to the offline-mode toggle (which lives in Settings,
  so the lobby can stay mounted): an online game lingered until the next
  reload. Reload on an offlineMode flip so entering offline immediately shows
  only device-local games.

Cold offline launch hanging on the splash (boot still fetches the profile over
the network) is the separate C2 offline-boot follow-up (needs a persisted
profile + a boot short-circuit).

ui/src/screens/Lobby.svelte

@@ -101,6 +101,18 @@
     // over the slower live stream; gating it keeps the card, its blink and the toast on one event.
     if (app.lastEvent && app.lastEvent.kind !== 'heartbeat') void load();
   });
+  // Reload when the deliberate offline mode flips (the toggle lives in Settings, so the lobby can
+  // stay mounted across the change): entering offline must immediately drop the online games and
+  // show only the device-local ones, and leaving it must refetch the online lobby. Guarded so the
+  // initial run — already covered by onMount — does not double-load.
+  let wasOffline = offlineMode.active;
+  $effect(() => {
+    const now = offlineMode.active;
+    if (now !== wasOffline) {
+      wasOffline = now;
+      void load();
+    }
+  });
 
   const myId = $derived(app.session?.userId ?? '');
   const groups = $derived(groupGames(games, myId, app.chatUnread));