podman quadlet supports healthchecks and healthcheck actions, configurable by the user. The podman role should allow the user to configure healthchecks. See https://issues.redhat.com/browse/RHELBU-1588
I have a wip of the podman role with support for quadlet, including networking and healthcheck (if using podman 4.5 or later). https://github.com/richm/linux-system-roles-podman/tree/quadlet It also contains an implementation of the quadlet-demo https://github.com/ygalblum/quadlet-demo, except using the podman role instead.