A few more observations after using the Z6II and Z-mount lenses for a few months.
Autofocus on native Z-mount lenses is fast and quiet. Continuous autofocus on the 24-70mm f/2.8 is as fast as any lens I've ever used, and is practically silent. Even if you listen for it in a quiet room, it's very difficult to hear any motor noise. The bigger surprise was the 85mm f/1.8, which unlike its F-mount equivalent, can focus fast enough to track fast moving subjects. It's a great portrait lens, but is perfectly suitable as a short tele walk around lens or even chasing my kid around in the yard. When using continuous autofocus, it makes a tiny bit of noise, but you still need to really listen for it, and it's nothing like any F-mount lens.
This one is a little nitpicky, but the focus ring on the Z-mount f/1.8 primes takes up almost the entire lens barrel. That's great when you want to use manual focus, but doesn't leave anything to hold when mounting or unmounting the lens. Whenever I switch lenses, I wind up turning the focus ring before remembering to grab closer to the body. It doesn't do any harm and probably just takes some getting used to, but after a few months with it I still grab the focus ring every time.
Lastly, I discovered yet another way the design of the FTZ adaptor is terrible. Most of my prior issues with it were solved by using an L-bracket permanently attached to the body. However, there is still the issue of trying to change lenses while the camera is mounted on a tripod. Even with the L-bracket providing a little more clearance, the FTZ adapter hits the Arca clamp on every tripod head I own from 3 different brands. This isn't something I do often, but occasionally I do not want to change the position of the camera even the slightest bit while switching lenses, and in those situations, I have no choice but to remove the camera from the tripod to do so if I want to switch between Z-mount and F-mount lenses. It's not really a new problem - the part that protrudes on the bottom just keeps getting in the way.
I will still conclude that I am very happy with the Z6II and Z-mount lenses, even with these minor complaints.