I'd love to hear from someone actively shooting video with these new cameras. I hear complaints about poor realtime autofocus in video and about noisy preamps in the audio section. On the other hand, my 70-200 VRII is great with the Z cameras—not as quiet as the S-series lenses, but quite usable, and performance from an optical and focus perspective is excellent.
I'd be using my legacy F lenses, 24-85 and 70-200 mostly.
How well-suited an F-mount Nikkor is to video autoficus depends very much on the lens. The motors were not designed with video autofocus in mind, and the constant micro-adjustments can sound alarmingly loud. For example, I have the 12-24mm DX Nikkor. I like it very much optically, and ir focusses well, but it's too noisy to use when I care about audio.
From my perspective, no DSLR or mirrorless camera I've ever tested has decent preamps. Their audio systems are all marginal at best. The Nikon is no exception.When I don't have an audio recordist on a shoot, I use a Sound Devices MixPre3 for audio, synced to the camera with a couple of Tentacle Sync timecode generators. That system works well and has truly excellent preamps and very good limiters. If $700 is too rich for your budget, any of the Zoom recorders will be a step up from the camera's audio system, as will the Tascam recorder, but they won't match the quality of the Sound Devices preamps.
As for autofocus performance in video, take a look at this:
I shot this PSA with a Z6 on a Moza Air 2 gimal, so both the girl and the camera were constantly in motion. Light was provided by just two practical fixtures with 75-watt bulbs. (It was critical to balance the ambient light so that the light from the iPhone screen played.) The lenses used were the 35mm and 50mm f/1.8 S lenses at f/2.0 or 2.2. It was shot in N-log at ISO 1600, if I remember correctly. As you see, autofocus performance was excellent. It helped a great deal to be able to adjust the speed of the autofocus to accomodate the changes of pace.