[client] login/register page 수정

### ISSUE
* Group: client,
* Type: feature
* Detail: 페이지별로 component화 하기, index.tsx에 있는 파일들을 app.tsx로 변환

### TODO
1. [ ] Component화 시키기
2. [ ] CSS
3. [ ] 기능 추가

### Estimated time
> Pick one

### `3h`

### Labels
* Estimated time: E: 3h
* Group : client,
* Week: week__3
* Urgency: High,

Start by inspecting the client login/register page and the files currently under index.tsx, then compare the existing structure with app.tsx. Confirm the intended page-level component boundaries and review the existing CSS and functionality before making changes. Done means the page is componentized, styled, and its listed functionality is added.

Written by the indexing model from the issue text.