You could add an IP TV software to your server to create channels that shuffle/loop infinitely. It takes a little work to configure the channels initially, but adding into Jellyfin is as simple as pasting the playlist (m3u) and listings (xml) urls into the live tv section. I’ve been mostly happy with Ersatz TV.

If it doesn’t do it now, submit a feature request so we developers have it on the radar: https://features.jellyfin.org/