Jellyfin is very conveniently packaged in docker, so while it may seem daunting, I highly recommend at least trying that route.
Running an nfs mount, docker or not, should be perfectly fine. Jellyfin just uses normal storage so won’t care if it’s nfs. No real special considerations with proxmox either, especially without worrying about a dedicated GPU. Just spin up a Debian guest and go.
No, the browser would still send YouTube.com as the host header. While yewtu.be could be configured to allow this to work, the TLS cert would not and the browser would get upset.