implement auth login and register with MongoDB

- Add AuthController login/register endpoints with error handling
- Implement AuthService with password validation and user creation
- Add MongoUserRepository with findByEmail and create methods
- Implement password hashing with bcrypt
- Add dotenv for environment variable support
- Add Docker Compose setup for MongoDB + Mongo Express
- Stub AuthMiddleware with fake user for testing
- Update CLAUDE.md with implementation status

CLAUDE.md

@@ -198,9 +198,44 @@ The repository pattern allows swapping databases:
 - Multiple calendars
 - CalDAV synchronization with external services
 
+## Development Environment
+
+### MongoDB (Docker)
+```bash
+cd apps/server/docker/mongo
+docker compose up -d                  # Start MongoDB + Mongo Express
+docker compose down                   # Stop services
+```
+- MongoDB: `localhost:27017` (root/mongoose)
+- Mongo Express UI: `localhost:8081` (admin/admin)
+
+### Environment Variables
+Server requires `.env` file in `apps/server/`:
+```
+JWT_SECRET=your-secret-key
+JWT_EXPIRES_IN=1h
+MONGODB_URI=mongodb://root:mongoose@localhost:27017/calchat?authSource=admin
+```
+
 ## Current Implementation Status
 
-**Backend:** Skeleton complete - all files exist with `throw new Error('Not implemented')` placeholders. Ready for step-by-step implementation.
+**Backend:**
+- **Implemented:**
+  - `AuthController`: login(), register() with error handling
+  - `AuthService`: login(), register() with password validation
+  - `MongoUserRepository`: findByEmail(), create()
+  - `utils/password`: hash(), compare() using bcrypt
+  - `utils/jwt`: signToken() (verifyToken() pending)
+  - `dotenv` integration for environment variables
+- **Stubbed (TODO):**
+  - `AuthMiddleware.authenticate()`: Currently uses fake user for testing
+  - `AuthController`: refresh(), logout()
+  - `AuthService`: refreshToken()
+  - All Chat and Event functionality
+- **Not started:**
+  - `ChatController`, `ChatService`, `MongoChatRepository`
+  - `EventController`, `EventService`, `MongoEventRepository`
+  - `ClaudeAdapter` (AI integration)
 
 **Shared:** Types and DTOs defined and exported.
 
@@ -216,6 +251,7 @@ The repository pattern allows swapping databases:
 ## Documentation
 
 Detailed architecture diagrams are in `docs/`:
+- `api-routes.md` - API endpoint overview (German)
 - `technisches_brainstorm.tex` - Technical concept document (German)
 - `architecture-class-diagram.puml` - Backend class diagram
 - `frontend-class-diagram.puml` - Frontend class diagram