What you are looking for is gpu pass through. You can do it with integrated graphics as well as dedicated. There is a lot of good documentation out there for proxmox to do this.

I would totally start with a hypervisor. The ability to spin up a new VM for an experiment or project far outweighs any downside. I use proxmox, but that’s mainly because it was the thing to do when I was starting out. There are a few options out there, including installing Debian and running kvm/qemu, which is basically what proxmox is. They all have the same functionality, just different UI/features. Lxc containers in proxmox help a lot as well, when you have a small service you want to run but don’t want to take up a VMs worth or resources. These also helped a lot.

Good luck

Hi I did that for Kodi, still using it and running in parallel other LXCs on the same machine. Scripts: https://github.com/mrrudy/proxmoxHelper Hope it helps.

I did this with proxmox. However I'm using a Nvidia gpu for passthrough. Was awhile ago I set it all up. I remember it being fairly complex. Here is a super basic instruction for it. Possibly incomplete.

Check you have iommu enabled in efi/bios. (For Intel - enable vt-d)

Install drivers if necessary (again nvidia)

Blacklist device on proxmox host

Setup GPU passthrough (vfio) - assign the card video and audio to the guest vm.

Start vm and test

If you are using onboard card, you can probably blacklist it and use it for your vm.. I'm not entirely sure how proxmox deals with losing its primary display.. I expect it'll cope ok. SSH for everything. Probably need to use virtio drivers. Install within guest..

Really.. prob best hosting a media server and having a client on the TV end.

Last time I had a vm with physical output was years ago, and it was an involved process. The thing you are looking for is PCI pass-through. Unless you are thinking closer to just running something like virtual box full screen?

Did you need your server to have hdmi output instead of running a normal jellyfin client? Would you consider a desktop os running server containers in docker or podman?

Yes and quite simple if your equipment supports it, the other VMS will not have access to the GPU if you do that.

VM or container? VM is easier and can be usually configured even via Proxmox GUI (Hardware - Add PCI). Various OSes need various levels of effort. Some Linux distros don't need any more config, Windows on the other hand required a custom GPU ROM on my system to work.

This can be done even with a single GPU, even the built in iGPU.

Never tried anything line that before but I feel like you'd be better off setting up VNC for it and connecting something lightweight to your TV and just interacting with the VM via VNC

What are you trying to display on the TV? I feel like most media can be handled better with something like PLEX rather than directly displaying it with an HDMI cord. Much easier to browse with a remote anyway.