The h265 hardware support is a lot less exciting than you might think. Most hardware that has support to encode it doesn’t even use the hardware encoders anyway because a software encoder produces a significantly better result. I would make sure you have CPU power to handle your transcoding, and I haven’t has any issues transcoding that resolution on my quite old Intel® Core™ i5-4590T CPU @ 2.00GHz.

A Raspi is probably not going to be enough for reliable video transcoding at high resolutions, but I haven’t tried it myself. You certainly have more upgrade path options with a mini-PC while still keeping a low power target.

I agree that distro is not very important if you’re running your services in Docker containers anyway. It’s mostly whatever you find comfortable. My personal recommendation is don’t get too creative unless you enjoy setting up servers. I tend to be conservative in my server OSs.