I use my Z9, D500and D850 the same way. I set Aperture Priority, Auto ISO and set the minimum shutter speed in Auto ISO.
My problem is that with the Z9, with the Nikon Z mount 100-400mm S lens attached, I found that the aperture I selected sometimes changed. If I set f5.6, it sometimes goes to f16 and smaller. I thought maybe my finger was inadvertently changing the aperture by turning the front command dial. But that does not happen with my D500 and D850.
I did not think I have set anything on the lens or the camera that could be causing this. But after checking lens settings in Custom Settings f2, I discovered that Lens Control Ring was set to Aperture. I changed that setting to Off. And that seems to have resolved the issue.
If you own and use Z mount tele lenses you might want to check all of the lens settings and make sure they are what you want.