Kodi is more self-contained, afaik, I have little experience with it.
But Jellyfin can also be used in this case, but it's really meant to be used as a server, something you access from various devices, usually not the one it's actually running on. Though you absolutely can do that, you'll just have to either use it in a browser, or install JMP as well as Jellyfin itself.
Jellyfin will get metadata and artwork via the internet, but once it has done this, there's no reason the server, media files, and client, can't all run on the deck, completely offline.
It will keep track of episode progress, allow you to mark stuff as favorite, make playlists...