If you're passing the iGPU to the VM then the host can't use it if the VM is on.
If your host supports SR IOV, then have a look at this repo: https://github.com/strongtz/i915-sriov-dkms
Installing this on Proxmox and your guest means the guest(s) and host to use the iGPU at the same time.
I'm not sure if it's in mainline somewhere but I had to install this DKMS to get it working.
Just realised your driving the TV with a VM. This probably isn't relevant then.