Web client's backend server has no health/readiness endpoint

[CloneOfAlex]

Which client?

Web

The problem

clients/web/server/server.ts exposes the proxy/API routes but nothing like /healthz -- there's no cheap way for an orchestrator (Docker, Kubernetes, a process manager) to check the backend process is up without exercising a real proxy/connect flow.

Solution you have in mind (optional)

Add a minimal unauthenticated GET /healthz (or /api/health) returning 200 plus basic status, matching the pattern used by most Node HTTP services.

Alternatives or workarounds you have tried

No response

Already built it locally?

No response

Before you submit

• I searched existing issues and this is not a duplicate.
• This is a request for the Inspector itself, not for the MCP specification or an SDK.