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

apps/server/src/services/AuthService.ts

@@ -7,11 +7,33 @@ export class AuthService {
   constructor(private userRepo: UserRepository) {}
 
   async login(data: LoginDTO): Promise<AuthResponse> {
-    throw new Error('Not implemented');
+    const user = await this.userRepo.findByEmail(data.email);
+    if (!user || !user.passwordHash) {
+      throw new Error('Invalid credentials');
+    }
+
+    const isValid = await password.compare(data.password, user.passwordHash);
+    if (!isValid) {
+      throw new Error('Invalid credentials');
+    }
+
+    return { user, accessToken: '' };
   }
 
   async register(data: CreateUserDTO): Promise<AuthResponse> {
-    throw new Error('Not implemented');
+    const existingUser = await this.userRepo.findByEmail(data.email);
+    if (existingUser) {
+      throw new Error('Email already exists');
+    }
+
+    const passwordHash = await password.hash(data.password);
+    const user = await this.userRepo.create({
+      email: data.email,
+      displayName: data.displayName,
+      passwordHash,
+    });
+
+    return { user, accessToken: '' };
   }
 
   async refreshToken(refreshToken: string): Promise<AuthResponse> {