[Task] LandingPage / 사이드바

### ISSUE
- Group: `client`
- Type: `feature`
- Detail: sideBar의 priofile 드롭다운설정 및 signIn 모달 설정, sideBar의 home버튼 기능 구현

### TODO
1. [ ] sideBar 간단하게 css 설정
2. [ ] profile 버튼 드롭다운 구현
3. [ ] signIn 클릭시 모달 구현
4. [ ] sideBar 홈버튼 기능 구현

### Estimated time

`2h`

### Labels
- Estimated time: `E: 2h`
- Group : `client`
- Sprint: `Sprint__NUMBER__`
- Urgency: `High`

Start with the LandingPage/sidebar area in the client repository and review the four TODO items together. Done means the sidebar has basic CSS, the profile control opens a dropdown, sign-in opens a modal, and the home button performs its intended navigation.

Written by the indexing model from the issue text.