There’s a lot of well meaning but not too well informed advice in here. Since one of your goals is gaming, stay away from Mint. It can be made to work (well), but you have to get there. It’s basically the recommendation people gave for decades, but there have been massive improvements through many distros while mint just kinda stood still. There’s still some things they do rather well though.
CachyOS will do what you want it to, and it is what I switched to like 8 months ago. It isn’t maintenance heavy at all if you don’t want it to be. I think I had to intervene once since I started using it, but that intervention was necessary or it wouldn’t have booted after updates. The official updater will tell you when that’s the case, as it lists critical news like that. Otherwise it just works, and it’s pre-configured and optimized for gaming. Under the hood it’s basically Arch, just without the fiddling of getting it to a usable state. Because of that they’re is also an enormous amount of information out there (Arch wiki) on how to do stuff.
Bazzite is a stark contrast in many ways as it’s an immutable distro, but also pre-configured and optimized (maybe not quite as much as CachyOS). It will also do what you want just fine. It is relatively “safe” due to the immutability, and updates are much rarer (and by definition always whole system updates). I don’t know exactly how you’d run your services, but assuming they are dockerized or similar that should be just fine, but please do some searching before if it does contain what you need in the base image (presumably docker and docker compose).













On Linux, running Jellyfin through docker with GPU acceleration works fine, yes. But you need some options/flags to pass access to the GPU to the inside of the container. Guides and/or docker tutorials exist and should contain that, as that’s basically the default setup these days.
As for Bazzite and Docker (I just checked), no it isn’t part of the base image and you can’t easily install it. That’s the downside of an immutable distro. I think podman is available, which is compatible and FOSS, but there may be caveats to using that. There is a bazzite version called bazzite-dx intended for developers, so that one would probably work fine for you out of the box. There shouldn’t be any real downside to using that compared to the mainline image, apart from being slightly larger cause all dev tools are installed, but do check that. My practical experience with Bazzite is limited.
My real recommendation is: just try it. Slap in a small/cheap SSD (~20 bucks) instead of whatever you got in there now, install CachyOS and try it out. Then install Bazzite and try it out. By “Try it out” I do mean setting up a copy of or a test-install of your required services (arr stack, jellyfin, …), to see if everything is as you’d expect. Possibly install more distros to try them out, then make up your mind and actually fully migrate, or if it doesn’t work out go back to your currently installed drive. Installing a linux distro takes like 10 minutes these days, then play around with however long you need. Since you already have it narrowed down to only 2 options anyway, that is most likely the best solution.