Implement Graceful Health Handling with Recovery

Enhance the HealthService with transparent caching and update the MCP server startup to handle unhealthy states gracefully.

Acceptance Criteria

HealthService Changes:

1. Add private caching fields: #cachedHealth, #lastCheckTime, #cacheDuration
2. Refactor current healthcheck() logic into #performHealthCheck()
3. Update healthcheck() to use cache (5 min TTL) before calling #performHealthCheck()
4. Add ensureHealthy() method that throws if status is 'unhealthy'
5. No changes to OpenAPI spec (caching is transparent)

MCP Server Changes:

6. Update mcp-stdio.mjs startup:

   • Call healthcheck() on startup
   • If unhealthy: log warnings but don't abort
   • Inform user server will continue but tools may fail

7. Update tool call handler:

   • Call HealthService.ensureHealthy() before callTool()
   • Catch and return error to agent if unhealthy
   • Use cached result (minimal overhead)

Benefits

• Performance: Avoids redundant health checks
• Resilience: Server doesn't crash on startup if gh missing
• Recovery: User can run gh auth login and tools will work
• UX: Clear errors guide users to fix issues