This could be a 2-step thing:

First add the a section to the service settings to configure Docker healthchecks to be able to attach them to the service: https://docs.docker.com/compose/compose-file/#healthcheck

And then generate a /status page under the panel domain (which is configurable and that's great for this), letting the admin to configure wether expose this to the public or remain private

I think this could be a VERY exploitable feature because it can also be used on the depends_on of Docker: https://docs.docker.com/compose/compose-file/#depends_on (check long syntax)