Generally intel has the best idle power consumption although amd won’t be terrible either. unless you already have an amd motherboard or cpu lying around I would recommend grabbing a 11th gen i5.

If you want to reduce your power idle power consumption undervolting won’t help you there, it will only reduce power consumption while under load. Generally the biggest killer for idle power consumption is actually your motherboard and for that reason try to find a smaller motherboard. Mini-itx is best but you’ll probably find that micro-atx is a lot cheaper while not sacrificing too much power draw.

I can’t say how useful your gtx 960 will be, I’d test it to see if it can encode/decode/transcode video fast enough for your needs. If it is fast enough then you can easily get away with an 8th/9th gen intel cpu you’ll find they are a lot cheaper, you could get an even older cpu as per Jellyfins hardware requirements but you’ll sacrifice some power consumption and probably not save that much money. 8th/9th gen CPU’s have pretty good power idle power consumption which is of course what should be targeted here.