Do you mean that all of the Z lenses ( not just S line ) perform better that the F mounts in general?
I don't think so, IMO.
I was testing AF performace of Sony's 200-600 with megadap adapter on Z9 against Z 100-400mm and Sony outperformed Nikon a bit. My Partner uses Sony 200-600 and Nikon Z 800mm and always says that AF of Sony on Nikon Z9 is faster than of Z800mm (photographing BIF)
I think, the biggest advantage of Z-lenses is in the camera correction and weight. And don't forget about marketing aspect, those Z-lenses must be good advertized to bring people to change their F-mount lens to Z-mount.
Each lens has also its own character, strong and weak points and in combination with particular camera under particular conditions works better or worse.
When you really start to test the lens (wih ISO chart and timer, etc..) then you may realise that F-mount lens can still compete with Z-mount very well. It is also important what works best
for you.
I also use 500mm PF, it is an excellent lens and performs very well. I bought Z 70-200/2.8 becasue of its close-up capability. I have 70-200/2.8 of Tamron, which is perhaps even sharper that Z-lens but it cannot focus so close. So,
for me to purchase a z-mount was an option and a wish, because I am using it for close-ups, too. But I think, that F-mount Nikon version (70-200/2.8 FL) has this feature as well and I am not sure if you need to change it.
Good way to make decisions is to rent the lenses for a couple of days and test it.