I used a 200-500 with an FTZ on a Z5, Z7ii and Z8. I never had any issues with autofocus, other than poor AF on the Z7ii with birds in flight. That was the camera, not the lens. I upgraded to the 180-600 nearly a year ago. I found that AF was a little better, but not by much. My advice, for what it's worth, is to go with the 180-600. If you already had the 200-500, that advice might be different. Look at my post in your other thread for a breakdown of the 100-400 and 180-600. The 200-500 is no longer sold by Nikon, I did see that B&H is still selling them new at $1200. Of course, you have to add $300 for the FTZ. That would bring this combo to $1500 vs $2100 for the 180-600.
I initially bought the 200-500 because there were no affordable Z mount long teles at the time. My opinion is that the 200-500 is a very good, sharp lens for the money, and it served me well for several years on my Z cameras. It is, however, an older design, and the newer Z lenses are definitely a step up.