Interesting, I have a Samsung TV but I'v never even considered running Jellyfin as a native app. I keep the TV off the internet so it can't be a spy box. The Chromecast with Google TV is so affordable and so great, I just use that everywhere. To be clear I'm not telling you you're wrong for wanting to do it on the TV, that's a personal preference, I'm just sharing how I do it in case it helps.
I ultimately ended up getting an nvidia shield, but at that point it solved my biggest gripe with plex so I just switched back to plex and have been happy with it.