perf: load calendar events instantly, sync CalDAV in background

Split loadEvents into two functions: loadEvents (instant DB read) and
syncAndReload (background CalDAV sync + reload). Events now appear
immediately when switching to the Calendar tab instead of waiting for
the CalDAV sync to complete.

apps/client/src/app/(tabs)/calendar.tsx

@@ -85,15 +85,9 @@ const Calendar = () => {
 
   const { events, setEvents, deleteEvent } = useEventsStore();
 
-  // Sync CalDAV then load events for current view
+  // Load events from local DB (fast, no network sync)
   const loadEvents = useCallback(async () => {
     try {
-      try {
-        await CaldavConfigService.sync();
-      } catch {
-        // No CalDAV config or sync failed — not critical
-      }
-
       // Calculate first visible day (up to 6 days before month start)
       const firstOfMonth = new Date(currentYear, monthIndex, 1);
       const dayOfWeek = firstOfMonth.getDay();
@@ -119,16 +113,25 @@ const Calendar = () => {
     }
   }, [monthIndex, currentYear, setEvents]);
 
-  // Load events when tab gains focus or month/year changes
-  // NOTE: Wrapper needed because loadEvents is async (returns Promise)
-  // and useFocusEffect expects a sync function (optionally returning cleanup)
+  // Sync CalDAV in background, then reload events
+  const syncAndReload = useCallback(async () => {
+    try {
+      await CaldavConfigService.sync();
+      await loadEvents();
+    } catch {
+      // Sync failed — not critical
+    }
+  }, [loadEvents]);
+
+  // Load events instantly on focus, then sync in background periodically
   useFocusEffect(
     useCallback(() => {
       loadEvents();
+      syncAndReload();
 
-      const interval = setInterval(loadEvents, 10_000);
+      const interval = setInterval(syncAndReload, 10_000);
       return () => clearInterval(interval);
-    }, [loadEvents]),
+    }, [loadEvents, syncAndReload]),
   );
 
   // Re-open overlay after back navigation from editEvent