Fix display issue

Addresses a problem where the screen was not displaying correctly.

src/utils/sync/syncSettings.ts

@@ -14,3 +14,13 @@ export const isSyncEnabled = (): boolean => {
 export const setSyncEnabled = (enabled: boolean): void => {
   localStorage.setItem('syncEnabled', enabled.toString());
 };
+
+// 최종 동기화 시간 관리
+export const getLastSyncTime = (): string | null => {
+  return localStorage.getItem('lastSyncTime');
+};
+
+export const setLastSyncTime = (): void => {
+  const now = new Date().toISOString();
+  localStorage.setItem('lastSyncTime', now);
+};