An intel nuc with an IGPU from the last few generations would do it no problem (even a pentium or i3 from the last few generations would be better than what you have by the sounds of it).
Or you can grab a cheap used quadro p600 or gt1050 (minimum model with hardware H265 NVENC support) and use that for transcoding or run an app like tdarr, unmanic or fileflows to convert your library to a direct streamable format in the background.
Why are you even requiring transcode is also something to look at, you should be trying to get your playback devices to play the raw files directly, that means a solid network infrastructure and properly configured software. If they are physically incapable of playing your 4k media then you need to look at upgrading them.
This all applies whether you are running plex, jellyfin, emby or whatever else.