It depends on what you mean by struggling but you can get pretty far with an 8th or 9th gen i5 and 16gb of RAM, would be a pretty cheap upgrade these days. The huge jump in quality for QuisckSync was between the 7th and 8th gen from what I remember so it doesn’t have to be new. If you are worried about power I think that it’s 65 or 70w for the 8th gen ones.
For what it’s worth, my current Plex machine is an 8500k with 32 gb of memory and a 250w power supply since it doesn’t have local storage and it has been running 24x7 for about 4 or so years now. I once load tested it for fun and I was able to do 7 or 8 4k transcodes and it wasn’t really its limit, I have no complaints haha.