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/game/CheckScreen.svelte

@@ -1,6 +1,7 @@
 <script lang="ts">
   import { onMount } from 'svelte';
   import { gateway } from '../lib/gateway';
+  import { gameSource, isLocalGameId } from '../lib/gamesource';
   import { handleError, showToast } from '../lib/app.svelte';
   import { t } from '../lib/i18n/index.svelte';
   import { alphabetLetters } from '../lib/alphabet';
@@ -20,8 +21,10 @@
 
   onMount(async () => {
     try {
-      // Include the alphabet so input sanitising + the check accept the variant's letters.
-      const st = await gateway.gameState(id, true);
+      // Include the alphabet so input sanitising + the check accept the variant's letters. Routed
+      // through gameSource so an offline (local) game resolves its state from the device, not the
+      // network.
+      const st = await gameSource(id).gameState(id, true);
       variant = st.game.variant;
     } catch (e) {
       handleError(e);
@@ -41,7 +44,7 @@
     cooling = true;
     setTimeout(() => (cooling = false), 5000);
     try {
-      const r = await gateway.checkWord(id, w, variant);
+      const r = await gameSource(id).checkWord(id, w, variant);
       checked.set(w, r.legal);
       result = { word: w, legal: r.legal };
     } catch (e) {
@@ -77,7 +80,11 @@
         : t('game.wordIllegal', { word: result.word })}
     </p>
     <div class="actions">
-      <button class="complain" onclick={complain}>{t('game.complain')}</button>
+      <!-- Complaints go to the admin over the network; a local (offline) game has no backend to
+           receive them, so the control is dropped there. -->
+      {#if !isLocalGameId(id)}
+        <button class="complain" onclick={complain}>{t('game.complain')}</button>
+      {/if}
       {#if result.legal}
         <a
           class="lookup"

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));