I have a GPU in a server, its a nvidia P400, that has 4 transcoding cores, can do h264 and hevc. It works fine with most software that uses ffmpeg to transcode, jellyfin uses ffmpeg. You dont need to run any displays to utilize the transcoding parts, running nvidia-smi will show you any processes using the GPU. I'm not sure about other cards but I have seen other people doing it. I'm not sure what cards will do AV1.

All my servers use ZFS for data storage, they have VPN's between each other (just /30 P2P's). I use zfs-snapshot to take snapshots every 15 minutes and nightly jobs that do a ZFS send to dump everything to another machine with some storage.