feat: add Korean (ko) language support

[cskwork]

Summary

Adds Korean (ko) as a selectable UI language alongside the existing English (en) and Chinese (zh). The default remains en — this PR only adds Korean as an option for users who want it.

Hi maintainers! I'm a Korean user who has been enjoying DeepTutor. I translated the entire UI into Korean and would love to contribute it upstream so other Korean users can benefit. Happy to iterate on wording or style if you have preferences.

Changes

Frontend (web/)

• New locales/ko/app.json — 859 keys, full parity with en/app.json
• New locales/ko/common.json
• Extended AppLanguage type union with "ko" in i18n/init.ts, context/AppShellContext.tsx, lib/datetime.ts, and the settings page
• Settings language picker now offers English / 中文 / 한국어
• Added ko-KR locale mapping in lib/datetime.ts
• Added language.korean label to en/common.json and zh/common.json for symmetry

Backend (deeptutor/)

• UISettings and LanguageUpdate Pydantic Literal extended to accept "ko" (default still "en")
• _normalize_language recognizes ko / korean / kr aliases

Translation notes

• Followed the zh/app.json convention of translating feature names (e.g., Deep Solve → 딥 솔브, Vision Solver → 비전 솔버, Co-Writer → 코라이터, Playground → 플레이그라운드)
• Kept universally-recognized technical acronyms in English (LLM, TTS, RAG, API Key, Base URL, gpt-4o, file paths)
• Verified 859/859 key parity with en/app.json via a parity check script
• npx tsc --noEmit passes cleanly in web/

Test plan

• Select 한국어 in Settings → Appearance and verify the UI switches
• Verify en / zh remain unaffected
• Verify the language selection persists across reloads
• Verify GET /api/v1/settings/ui and PUT /api/v1/settings/ui accept "ko"
• Spot-check a few screens (Dashboard, Settings, Co-Writer, TutorBot, Solver) for layout regressions with longer Korean strings

[pancacake]

Thanks for your contribution! Howver, DeepTutor is updating frequently nowadays, so i'll try to merge this when our update frequency is lower.