Filestore is not an RSP application, nor does it (generally) run in Kubernetes.
All current filestore implementations are simply implementations of NFS that are mounted into RSP Pods (both JupyterLab user Pods and application Pods) by
There is nothing in the filestore that mandates NFS. What is required is simply something that can present some storage to user and application Pods as a POSIX filesystem. To this point, NFS has been the most convenient way to accomplish that, but it is certainly not fundamental to the concept.