[router] Health check on worker before added to the router

[ByronHsu]

Motivation

1. Users call /add_worker
2. The router performs health check on the worker periodically
3. If passed, the worker is added to the router

Modifications

Checklist

• Format your code according to the Contributor Guide.
• Add unit tests as outlined in the Contributor Guide.
• Update documentation as needed, including docstrings or example tutorials.