Beware that using http://node:8983/api/node/health?requireHealthyCores=true for your liveness assumes that ZK is up and running. We are all hoping that ZK is never down, but if it happens, your Solr liveness probe will start to fail too, and K8S will restart all our Solr, adding instability to a cluster that is already in a bad shape.
We've configured our liveness to /solr/admin/info/system too, and we rely on ZK liveness probe to restart ZK quickly if there is an issue. Liveness probes should never rely on a subsystem being up, else all your services will go down one after the other. Regards, Mathieu