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.

I’m pretty sure sensi thermostats, when controlled by home assistant, do what you want. I haven’t confirmed they don’t still try to phone home, but that could be dealt with by some firewall rules. Other thermostats that support homekit should also work.

I do almost exactly the same, except I have opnsense running on a cheap dual nic mini PC so I don’t have that dependency on my proxmox servers. The unifi stuff does need a controller, but they publish a free app that you can run instead of getting their hardware.