Thin clients are the best for this. You can take your pick on an abundant of options on eBay.
Jellyfin isn't that power hungry, and it would run on a rPi if you set it up right. You're only problems are when it decides to transcoder file and you can get around that by using Kodi with the jellyfin add-on. (And choosing the native paths option. Kodi grabs all the data via, SMB, NFS, etc)
This way you can use Jellyfin as a media enrichment solution, not worry about the CPU or GPU encoding and just worry about watching everything.