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/package.json

@@ -5,26 +5,33 @@
   "scripts": {
     "dev": "tsx watch src/app.ts",
     "build": "tsc",
-    "start": "node dist/app.js"
+    "start": "node dist/app.js",
+    "test": "jest"
   },
   "dependencies": {
     "@calchat/shared": "*",
     "bcrypt": "^6.0.0",
     "dotenv": "^16.4.7",
     "express": "^5.2.1",
+    "ical.js": "^2.2.1",
     "jsonwebtoken": "^9.0.3",
     "mongoose": "^9.1.1",
     "openai": "^6.15.0",
     "pino": "^10.1.1",
     "pino-http": "^11.0.0",
-    "rrule": "^2.8.1"
+    "rrule": "^2.8.1",
+    "tsdav": "^2.1.6"
   },
   "devDependencies": {
     "@types/bcrypt": "^6.0.0",
     "@types/express": "^5.0.6",
+    "@types/ical": "^0.8.3",
+    "@types/jest": "^30.0.0",
     "@types/jsonwebtoken": "^9.0.10",
     "@types/node": "^24.10.1",
+    "jest": "^30.2.0",
     "pino-pretty": "^13.1.3",
+    "ts-jest": "^29.4.6",
     "tsx": "^4.21.0",
     "typescript": "^5.9.3"
   }