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/repositories/mongo/models/CaldavConfigModel.ts

@@ -0,0 +1,22 @@
+import { CaldavConfig } from "@calchat/shared";
+import mongoose, { Document, Schema } from "mongoose";
+
+export interface CaldavConfigDocument extends CaldavConfig, Document {
+  toJSON(): CaldavConfig;
+}
+
+const CaldavConfigSchema = new Schema<CaldavConfigDocument>(
+  {
+    userId: { type: String, required: true, index: true },
+    serverUrl: { type: String, required: true },
+    username: { type: String, required: true },
+    password: { type: String, required: true },
+    syncIntervalSeconds: { type: Number },
+  },
+  { _id: false },
+);
+
+export const CaldavConfigModel = mongoose.model<CaldavConfigDocument>(
+  "CaldavConfig",
+  CaldavConfigSchema,
+);