After being too used to the streaming app experience, I wanted the same thing for my own library. You don't need to use the transcoding feature but the Netflix experience is a nice upgrade. The Jellyfin server doesn't need much for resources either (if you aren't transcoding), people run it on raspberry pis with external harddrives attached. Once nice thing is that I often forget about the stuff I've downloaded, Jellyfin has a "recently added" section and will also remember where I've left off with a "continue watching" section and also a "next up" section showing the next episode in series I'm watching. Since I have sonarr subscribed to currently airing TV shows, the latest episode will appear there after its been downloaded.

The annoying thing is that Jellyfin is particular about how your TV shows are organized. If you just dump whole seasons into one directory, that's fine but if you have individual episodes, they need to be organized by Title/Season #/Episode.mkv. The good thing about Sonarr is that it will make a second library directory for you comprised of hardlinks organized in the right structure. Plex is less picky, it seems to recognize files no matter how messy your downloads folder is but Plex has infected their client with ads and freemium garbage of late. Obviously if you use usenet, this isn't a huge problem, you can do whatever you want with your files once downloaded.