test(offline): e2e hotseat flow + fix $state-proxy persist

Add the Playwright mock e2e for offline pass-and-play (Chromium+WebKit):
create a 2-seat hotseat with a PIN-locked seat, verify the rack is
withheld, unlock (wrong then right PIN), host-skip the current turn, and
terminate from the lobby behind the master PIN.

The e2e surfaced a persistence bug: the roster PINs are $state proxies,
which fail structured-clone on the IndexedDB put (silently — best-effort
store), so a created hotseat game vanished on reload. Snapshot the seats
+ host PIN to plain objects at the create() call site.

ui/src/screens/NewGame.svelte

@@ -230,15 +230,18 @@
         return;
       }
       const id = newLocalGameId();
+      // Snapshot the roster + PINs to plain objects: the rows/pins are $state proxies, and a proxy
+      // fails structured-clone when the record is persisted to IndexedDB (silently, since the store
+      // is best-effort) — so the game would vanish on reload. See lib/localgame/store.
       await localSource.create({
         id,
         variant: inviteVariant,
         dictVersion: version,
         seed: randomSeed(),
         multipleWords: multipleWordsForRequest(inviteVariant, multipleWords),
-        seats: buildSeats(rows),
+        seats: $state.snapshot(buildSeats(rows)),
         hotseat: true,
-        hostPin,
+        hostPin: hostPin ? $state.snapshot(hostPin) : undefined,
       });
       navigate(`/game/${id}`);
     } catch (e) {