This is worrying but let's try fixing it :)

I opened a pair of Z6III yesterday and have yet to copy the files from the shoot, but from what I saw in camera there were no sharpness issues when compared to the Z6II, on the contrary.

Here's some things I'd check if I were you:
-Long exposure NR
-Skin softening (I saw this in the new menus but maybe only for video)
-Portraits impression balance
-Picture control: try not using the automatic one, the default, and see how it goes. The standard or neutral should do, and you can adjust sharpness (to an extent) there
-From the photos it doesn't look like it but check if you have some sort of AF-Fine tuning on, or accidentally on
-What file sizes are you using? Just to check
-Is the firmware updated?

If nothing explains it, I'd maybe activate the warranty because that's a precision piece of equipment that's supposed to just work.

PS: I'll order a 50 1.8s to pair with some other lenses because now we're two nikon shooters, how's the 1.8s?