feat: add CalDAV synchronization with automatic sync

- Add CaldavService with tsdav/ical.js for CalDAV server communication
- Add CaldavController, CaldavRepository, and caldav routes
- Add client-side CaldavConfigService with sync(), config CRUD
- Add CalDAV settings UI with config load/save in settings screen
- Sync on login, auto-login (AuthGuard), periodic timer (calendar), and sync button
- Push single events to CalDAV on server-side create/update/delete
- Push all events to CalDAV after chat event confirmation
- Refactor ChatService to use EventService instead of direct EventRepository
- Rename CalDav/calDav to Caldav/caldav for consistent naming
- Add Radicale Docker setup for local CalDAV testing
- Update PlantUML diagrams and CLAUDE.md with CalDAV architecture

apps/server/src/services/EventService.ts

@@ -24,10 +24,18 @@ export class EventService {
     return event;
   }
 
+  async findByCaldavUUID(userId: string, caldavUUID: string): Promise<CalendarEvent | null> {
+    return this.eventRepo.findByCaldavUUID(userId, caldavUUID);
+  }
+
   async getAll(userId: string): Promise<CalendarEvent[]> {
     return this.eventRepo.findByUserId(userId);
   }
 
+  async searchByTitle(userId: string, query: string): Promise<CalendarEvent[]> {
+    return this.eventRepo.searchByTitle(userId, query);
+  }
+
   async getByDateRange(
     userId: string,
     startDate: Date,