I had both the original 80-400 and the later 80-400 AFS lenses. The 80-400 AFS was significantly better, both optically and for AF. I used mine mostly on a D500. The AF was faster than the AF with my 200-500 and it was easier to carry around on walks/hikes and use in kayaks and canoes. The 80-400 was probably best from 80-300 or so. A bit softer at 400, but usable. I have many images that I like from it.At the risk of going slightly off topic for just a second, based on your obvious range of experience and you mentioning shooting golf, what do you think about the AF-S NIKKOR 80-400mm f/4.5-5.6G ED VR as a buy for general use including golf and catching the occassional BIF images? I didn't know they even existed until a week ago but it fits a gap in my lens range I am looking to fill.
I never tried my 80-400 on a Z mirrorless body. Should have. But I wonder whether it might perform better in some ways on a Z body than on a DSLR, since the Z body AFs on the sensor, which is a bit like focus tuning and could help at any focal length. One counter to this is that using the 80-400 on a DX body like the D500 probably uses the best part of the lens — i.e., the center and skips the FX corners.
One other point. The 80-400 AFS has a reputation for copy variance. Mine was pretty good. I was on a trip to Galapagos with it in 2017. 4 or 5 of the participants and one of the leaders had a 80-400 along. The leader looked at each of the 80-400s and felt that a couple were fine as is (including mine), a couple of them needed focus tuning (not so easy to do with a zoom) and felt that one was simply not sharp.
So if you can, you may want to try the 80-400 you are considering before buying it, to see how it performs.
If you do not often need 400 mm, the 70-300 AF-P FX lens is a nice light telephoto that performs well above what its price might suggest. The FX version is better than the DX version. While I no longer have the 80-400 or the 200-500, I’ve kept my 70-300 and use it on a mirrorless body at times, since there is no small, light Z mount telephoto zoom yet.
The 100-400 in Z mount is a very nice lens and I have enjoyed using it a lot. I think it is better optically than the 80-400, but while it will work great on your Z9, it will not work on your D500.
Good luck.