implement backend skeleton with MongoDB and Claude AI integration

- Add controllers (Auth, Chat, Event) with placeholder implementations
- Add services (Auth, Chat, Event) with business logic interfaces
- Add repositories with MongoDB/Mongoose models (User, Event, Chat)
- Add middleware for JWT authentication
- Add Claude AI adapter implementing AIProvider interface
- Add utility modules for JWT and password handling
- Add shared types and DTOs for User, CalendarEvent, ChatMessage
- Configure routes with proper endpoint structure
- Update app.ts with dependency injection setup
- Add required dependencies: mongoose, bcrypt, jsonwebtoken, @anthropic-ai/sdk

apps/server/src/repositories/mongo/models/EventModel.ts

@@ -0,0 +1,56 @@
+import mongoose, { Schema, Document } from 'mongoose';
+import { CalendarEvent } from '@caldav/shared';
+
+export interface EventDocument extends Omit<CalendarEvent, 'id'>, Document {}
+
+const EventSchema = new Schema<EventDocument>(
+  {
+    userId: {
+      type: String,
+      required: true,
+      index: true,
+    },
+    title: {
+      type: String,
+      required: true,
+      trim: true,
+    },
+    description: {
+      type: String,
+      trim: true,
+    },
+    startTime: {
+      type: Date,
+      required: true,
+    },
+    endTime: {
+      type: Date,
+      required: true,
+    },
+    note: {
+      type: String,
+    },
+    isRecurring: {
+      type: Boolean,
+      default: false,
+    },
+    recurrenceRule: {
+      type: String,
+    },
+  },
+  {
+    timestamps: true,
+    toJSON: {
+      transform: (_, ret: Record<string, unknown>) => {
+        ret.id = String(ret._id);
+        delete ret._id;
+        delete ret.__v;
+        return ret;
+      },
+    },
+  }
+);
+
+EventSchema.index({ userId: 1, startTime: 1, endTime: 1 });
+
+export const EventModel = mongoose.model<EventDocument>('Event', EventSchema);