Refactor backend health check and remove context usage

[humanagent]

Remove centralized backend health monitoring and implement direct health checks in the frontend health endpoint

• Implements cache prevention headers and enhanced validation in the /health endpoint in route.ts
• Removes the centralized BackendHealthProvider context from backend-health-context.tsx
• Updates ConnectionInfo component to manage its own health check state in ConnectionInfo.tsx
• Removes backend health status checks from GroupChat component in GroupChat.tsx
• Removes section headings from Page.tsx
• Removes BackendHealthProvider from provider composition in index.tsx

📍Where to Start

Start with the health endpoint implementation in route.ts, which contains the core health check logic and cache prevention mechanisms.

---

Macroscope summarized 3c2ed7b.