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/interfaces/EventRepository.ts

@@ -8,6 +8,7 @@ export interface EventRepository {
     startDate: Date,
     endDate: Date,
   ): Promise<CalendarEvent[]>;
+  findByCaldavUUID(userId: string, caldavUUID: string): Promise<CalendarEvent | null>;
   searchByTitle(userId: string, query: string): Promise<CalendarEvent[]>;
   create(userId: string, data: CreateEventDTO): Promise<CalendarEvent>;
   update(id: string, data: UpdateEventDTO): Promise<CalendarEvent | null>;