Thanks, this has resolved the issue.
It worked well.
I guess, I need to explore the local-lvm a bit more.
It looks like local-lvm has...
Thanks @fabian, I guess in my case (please help me where I am going into a wrong direction).
Since the set-up is rather "unstable" and cannot rely on "always on" capability I would need to have each server pointing out to the own local-lvm.
In this set-up there is no "sharing" possible.
I'm new to Proxmox and this question might be basic, still need help, as could not find the answer by myself.
3 Proxmox systems have been installed on individual (rather small boxes).
2 systems (pve01, pve02) are based on N5100 (2LAN ports) and another one is a bit beefier...