docs: Update README with Playground frontend and current state

- Documentation: Playground Backend 링크 유지, Frontend/Monitoring/Settings 언급
- Playground 섹션: 통합 Chat UI, Agentic 모드, Google OAuth, 모니터링 대시보드

Author: leebeanbin

README.md

@@ -21,6 +21,9 @@
 
 - 💡 **[Examples](examples/)** - 15+ working examples
 - 📦 **[PyPI Package](https://pypi.org/project/beanllm/)** - Installation and releases
+- 🌐 **[Playground](playground/backend/README.md)** - 통합 Chat UI + FastAPI 백엔드
+  - **Backend**: FastAPI, Agentic Chat(의도 분류/도구 라우팅), Google OAuth, API 키 동적 설정, 모니터링 API
+  - **Frontend**: Next.js 15 + React 19, Settings(API 키/Google 연결), Monitoring 대시보드, 반응형 Chat UI
 
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