10. [task] 로그인 (page) - OAuth (component)

### ISSUE
- Group: `client`
-Type: `feature`
-Detail: 로그인 페이지에서 OAuth 로그인 구현 컴포넌트

### TODO
1. [ ] github(bareminimum)
2. [ ] kakao(advanced)
3. [ ] 로그인 성공하면 홈화면으로 이동

### Estimated time
>Pick one

### `0.5h`

Start by locating the client login page and its OAuth-related component or routing entry point. Implement the GitHub minimum requirement first, then the advanced Kakao option if supported by the project. Done means successful login redirects to the home screen; verify both OAuth flows manually.

Written by the indexing model from the issue text.