feat: add inspection_expiry/has_etc/tire_type fields, icons in schedule view, and WebSocket real-time sync

Co-authored-by: pdf114514 <57948770+pdf114514@users.noreply.github.com>
Agent-Logs-Url: https://github.com/pdf114514/CarReservation/sessions/6d0f25ae-6db4-4937-ae2b-6674456a5ca1

frontend/src/utils/carUtils.js

@@ -0,0 +1,13 @@
+/**
+ * Returns true if the given inspection expiry date string is within 1 month
+ * from today (or already past).
+ * @param {string} inspectionExpiry - ISO date string (YYYY-MM-DD) or empty
+ * @returns {boolean}
+ */
+export function isInspectionExpirySoon(inspectionExpiry) {
+  if (!inspectionExpiry) return false;
+  const expiry = new Date(inspectionExpiry);
+  const oneMonthLater = new Date();
+  oneMonthLater.setMonth(oneMonthLater.getMonth() + 1);
+  return expiry <= oneMonthLater;
+}