Some more details may help here.
What printer is it and what’s it reaching out for?
As said, setting up static ip and removing the gateway will usually be enough. Vlans are the better option but steeper learning. I’d be interested to find out what it’s doing though. Knowing what you’re working with may help others advise you more specifically.
If it’s checking to find time or for updates then it’s probably harmless. Do you need internet to enable any features like remote send or monitoring and the like?
With the price of ssds what they are now for a small 100gb why bother with the additional setup and potentially failure points.
I’ve run esxi through network and even that wasn’t fun with longish boot times. I certainly wouldn’t like to run proxmox that way. These days there’s really no reason not to have “some” fast direct storage in each server even if it’s just used mainly as cache.
What you’re looking for is possible but to me the saving of $20 ish per machine just isn’t worth introducing more headaches.