[프론트엔드] <SideBar> 소셜 로그인 기능 구현

## ISSUE
- Group: `client`
- Type: `feature`
- Detail: `Side Bar: 소셜 로그인 페이지`

## TODO
- [ ] OAuth: 소셜 로그인 페이지로 이동
post/ {Authorization: AuthorizationCode}
- [ ] 토큰 상태 변경
- [ ] 로그인 상태 변경

## Estimated time

### `3hs`

## Labels
Estimated time: E: `3hs`
Group : `client`
Sprint: `Sprint 2`
Urgency: `advanced`

Start at the client-side SideBar entry point and trace how it should navigate to the social login page. Review the OAuth POST flow using the authorization code, then follow the token and login-state handling. Done means the page navigation, token state, and login state are updated for a social login.

Written by the indexing model from the issue text.