I cant find much information on internet on Akka cluster application health
Is it same like kubernetes readinessProbe? If yes, then what is the frequency of call? When ready function of ReadinessCheck gets called - when each node of cluster is up and joined the cluster or before it? Can I configure it under kubernetes readinessProbe if my akka cluster is on top of kubernetes?
The documentation you refer to describes a way to introduce health- and readiness endpoints in your application. The purpose of those endpoints is that they can be called by, typically, the Kubernetes health and readyness checks. The library will not call these endpoints itself, it only provides them.
When deploying your application on Kubernetes, indeed it would make sense to add health and readiness checks for this application to Kubernetes, which use these endpoints to tell whether your application is ready to start accepting traffic.