Yes, you can run Jellyfin from your Steam Machine. It's right there in the Discovery software center.
Only quirk, other than all the quirks and fussiness Jellyfin has on it's folder structure, is that it's installed with flatpak so you gotta explicitly grant it permission to read your data directory if it isn't the default one.
Mine, for instance, is at ~/data/media so I have to:
And have to do that after install, but before setup-wizard.
Jellyfin is just nightmarish for copying to a new machine in general. Don't try and copy the config. Just be sure to always store your thumbnail images etc. alongside the files and accept it's going to be a rescan a loss of all your watched-already data I guess.
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