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/docker/radicale/docker-compose.yml

@@ -0,0 +1,25 @@
+name: Radicale
+services:
+    radicale:
+        image: ghcr.io/kozea/radicale:stable
+        ports:
+        - 5232:5232
+        volumes:
+          - config:/etc/radicale
+          - data:/var/lib/radicale
+
+volumes:
+  config:
+    name: radicale-config
+    driver: local
+    driver_opts:
+      type: none
+      o: bind
+      device: ./config
+  data:
+    name: radicale-data
+    driver: local
+    driver_opts:
+      type: none
+      o: bind
+      device: ./data