I have a couple suggestions, the first may be obvious, but Jellyfin settings can be pretty convoluted so you never know.

What you may be looking for is the difference between “Up Next” and “Latest” (or “Recently Added?” can’t remember exactly, I already powered down for the night). You can add one or both as sections to your home page, which should keep all your latest additions front and center, while also keeping track of the stuff you’re currently watching, if you want.

My more advanced suggestion is to check out the SmartPlaylists plugin. It may not do exactly what you’re imagining, but it’s surprisingly powerful once you get used to the slightly weird UI and rules setup. You can build playlists based on very specific fine-tuned rules, so you could pretty easily set up playlists to only show what you want to see, and they automatically update as your library changes, which is pretty cool.

Really interesting that you’ve encountered this, I have no trouble at all watching super-high bitrate media in Infuse. I may be spoiled with my gigabit internet, but the Apple TV caches entire 4K Blu-rays in minutes on my local network (you can watch the seek bar fill up, it’s really satisfying) so I never thought about this. I’m curious why this hits some users and not others.

As others have said, Jellyfin server with Infuse as the player on Apple TV is the best experience, especially for Dolby Vision, which works flawlessly. Anyone in your house should find the interface super-easy to navigate. But if the price of Infuse turns you off (which I get), the native Jellyfin app on Apple TV isn’t terrible (Swiftfin), and there are some other less-polished apps for way cheaper than Infuse (MrMc I think?). The native Jellyfin app struggles with Dolby Vision, otherwise you’ll have no trouble with it, but definitely a slightly clunkier experience than with Infuse. I personally find the price of Infuse way too high, but I can’t argue with the stability and slick UI.

The Apple TV also caches content really well, so you won’t run into any issues with high bitrates over streaming. I regularly watch full 4K Dolby Vision Blu-rays (50-70 GB files) with buttery smooth playback, no issues at all.