feat: 학습 페이지 구현

[hani0903]

🔍 작업 유형

• 🛠 feat (새로운 기능)
• 🔧 fix (버그 수정)
• ✨ enhancement (기존 기능 개선)
• ⚙️ chore (빌드, 설정 변경)
• 📝 docs (문서 수정)
• 🤝🏻 style (코드 포맷팅, 세미콜론 누락 등)
• 💻 refactor (코드 리팩토링)
• ✅ test (테스트 추가/수정)

📄 작업 내용

• 학습 페이지를 구현하였습니다.

🔗 관련 이슈

• Closes #이슈번호

✅ 체크리스트

• 코드가 정상적으로 동작합니다
• 변경 사항이 기존 기능에 영향을 주지 않습니다
• 새로운 테스트를 추가했습니다 (해당하는 경우)
• 문서를 업데이트했습니다 (해당하는 경우)

🖼️ 🖥 구현 결과 (선택사항)

✔ 리뷰 요구사항

📋 참고 문서

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Project	Deployment	Preview	Comments	Updated (UTC)
gravit	Error			Sep 9, 2025 3:06pm
web	Error			Sep 9, 2025 3:06pm

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Currently processing new changes in this PR. This may take a few minutes, please wait...

📥 Commits

Reviewing files that changed from the base of the PR and between 30d73e2 and f610a1c.

⛔ Files ignored due to path filters (2)

• src/assets/icons/button/floating-check.svg is excluded by !**/*.svg
• src/assets/icons/button/floating-next.svg is excluded by !**/*.svg

📒 Files selected for processing (24)

• src/api/fetchProblems.ts (1 hunks)
• src/components/chapter-page/Tooltip.tsx (1 hunks)
• src/components/lesson-page/FloatingButton.tsx (1 hunks)
• src/components/lesson-page/Header.tsx (1 hunks)
• src/components/lesson-page/LessonProgress.tsx (1 hunks)
• src/components/lesson-page/OptionItem.tsx (1 hunks)
• src/components/lesson-page/OptionsList.tsx (1 hunks)
• src/components/lesson-page/problem/AnswerInput.tsx (1 hunks)
• src/components/lesson-page/problem/AnswerSection.tsx (1 hunks)
• src/components/modal/LessonQuitModal.tsx (1 hunks)
• src/context/ProblemContext.tsx (1 hunks)
• src/hooks/useAnswerState.tsx (1 hunks)
• src/hooks/useAuthState.tsx (1 hunks)
• src/layouts/NoHeaderLayout.tsx (1 hunks)
• src/pages/ChapterDetailPage.tsx (2 hunks)
• src/pages/MainPage.tsx (1 hunks)
• src/pages/ProblemPage.tsx (1 hunks)
• src/routes/router.tsx (1 hunks)
• src/types/@common/problem.ts (1 hunks)
• src/types/api/problem-response.ts (1 hunks)
• src/types/transformers/transformProblems.ts (1 hunks)
• src/utils/cn.ts (1 hunks)
• src/utils/formatTime.ts (1 hunks)
• src/utils/parseAnswers.ts (1 hunks)

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