회원가입 라우팅 및 기능 구현

### ISSUE

- Group: `server`
- Type: `feature`
- Detail: 회원가입 라우팅 및 기능 구현

### TODO

- [x] 회원가입 성공 시, 유저 데이터 전송 (201)
- [x] 중복된 이메일의 경우, 메세지 발송 (409)
- [x] 서버 에러의 경우, error 발송 (500)

### Estimated time
>Pick one

### `2h`

### Labels

- Estimated time: `E: 2h`
- Group: `server`
- Sprint: `Sprint__NUMBER__2`
- Urgency: `High`

The issue does not name files, tests, or a specific entry point. Start by locating the server's signup route and its request handling, then verify the listed success, duplicate-email, and server-error outcomes. Done means the signup routing and behavior satisfy all three checked requirements.

Written by the indexing model from the issue text.