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/controllers/ChatController.ts

@@ -8,13 +8,17 @@ import {
   RecurringDeleteMode,
 } from "@calchat/shared";
 import { ChatService } from "../services";
+import { CaldavService } from "../services/CaldavService";
 import { createLogger } from "../logging";
 import { AuthenticatedRequest } from "./AuthMiddleware";
 
 const log = createLogger("ChatController");
 
 export class ChatController {
-  constructor(private chatService: ChatService) {}
+  constructor(
+    private chatService: ChatService,
+    private caldavService: CaldavService,
+  ) {}
 
   async sendMessage(req: AuthenticatedRequest, res: Response): Promise<void> {
     try {
@@ -68,6 +72,16 @@ export class ChatController {
         deleteMode,
         occurrenceDate,
       );
+
+      // Sync confirmed event to CalDAV
+      try {
+        if (await this.caldavService.getConfig(userId)) {
+          await this.caldavService.pushAll(userId);
+        }
+      } catch (error) {
+        log.error({ error, userId }, "CalDAV push after confirm failed");
+      }
+
       res.json(response);
     } catch (error) {
       log.error(