Linux is usually lighter on hardware, so in theory you have more performance left for games. I doubt it’s noticeable though and I certainly didnt notice any difference except for some games like GTA 4 and Sims 3. They run a lot better on Linux than on Windows.
Which kernel do you use on Debian? IIRC support for Intel Arc was added in 6.0 or higher. I am using Proxmox (based on Debian) and I had to upgrade from 5.15 to 6.2 kernel to get hardware decoding to work. Have you checked the Jellyfin manual? It’s pretty elaborate on how to get Intel QSV working.