Well, I would say ~most~ efficient would be an ARM variant of some kind, but I'm guessing you want to stick with x86, and finding PCI slots on an ARM is going to be challenging. Barring that, I would try to find a U-package Intel die, but that may be difficult to match with available PCI slots.
When you are looking at idle power - the CPU is going to be a big contributor, but like LazyGamer alludes to - everything else is going to add up to a lot more - particularly RAM, whatever you have plugged into those PCI slots, etc.
From what I can gather, a typical Zen3 or Alder Lake desktop-class build are going to idle in the 30-60W range.
This is a fairly interesting read. I don't think core count or anything are really going to change your idle power much - everything on the CPU package is going to go into low power state anyway, so the difference between a Core i9 and Core i5 - at idle - isn't going to be much, if anything really measurable. Peak power - totally different animal, but that isn't the typical condition here.
I would also guess that a more recent generation of chip is going to be more efficient than an older one - just because of improvements in power management. I didn't pull any data to back this up, but I don't think it would be too hard to back it up.
So with that in mind, I'd go get whatever quad core Alder Lake or Zen3 you can find, throw it in with the slowest/most efficient RAM you can find, with the fewest sticks you can live with - if you can live with single channel all the better. And set any HDDs and SSDs to some aggressive power saving settings.
I don't know off hand of any way to really check power draw of specific motherboards - that would be interesting. I would hope that disabling all the stuff you don't need (extra NICs, onboard Sound, etc) would help minorly - even a watt or two adds up over the course of a few years.
That said, it's really hard to beat an ARM server that sips on about 6W at full load.
This article might be of some interest.
That last linked article also lead me to this:
https://www.asrock.com/mb/Intel/J4105M/ , which fits your requirements at supposedly scores about 2900 on passmark. This is an older package, late '17/early '18, so there may be updated ones.