feat: restructure client-side code

src/server/game/sync.js

@@ -0,0 +1,13 @@
+import { broadcast } from './state.js';
+
+export function startSyncTimer(room) {
+  if (room.syncTimer) clearInterval(room.syncTimer);
+  room.syncTimer = setInterval(() => {
+    if (room.state.status !== 'playing' || !room.state.currentTrack || !room.state.trackStartAt || room.state.paused) return;
+    broadcast(room, 'sync', { startAt: room.state.trackStartAt, serverNow: Date.now() });
+  }, 1000);
+}
+
+export function stopSyncTimer(room) {
+  if (room.syncTimer) { clearInterval(room.syncTimer); room.syncTimer = null; }
+}