Actually I got some of these (exact same model) for cheap from a business that went down 2 months ago.
I didn‘t have the time to properly test them out, but I threw plain debian on one of them. But I had to fiddle around with several settings in the bios/uefi first before getting it running.
As proxmox is based on debian, so I don‘t see a reason for it not to work.
I try to provide more information tomorrow - it‘s quite late in UTC+1.

This sound like you already mentioned the solution: A mini PC with several Ports and SSH into it via Vscode