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/client/src/app/login.tsx

@@ -4,6 +4,7 @@ import { Link, router } from "expo-router";
 import BaseBackground from "../components/BaseBackground";
 import AuthButton from "../components/AuthButton";
 import { AuthService } from "../services";
+import { CaldavConfigService } from "../services/CaldavConfigService";
 import { useThemeStore } from "../stores/ThemeStore";
 
 const LoginScreen = () => {
@@ -24,6 +25,11 @@ const LoginScreen = () => {
     setIsLoading(true);
     try {
       await AuthService.login({ identifier, password });
+      try {
+        await CaldavConfigService.sync();
+      } catch {
+        // No CalDAV config or sync failed — not critical
+      }
       router.replace("/(tabs)/chat");
     } catch {
       setError("Anmeldung fehlgeschlagen. Überprüfe deine Zugangsdaten.");