From autofocus prospective, does Z6-iii exceeds other two options?
Back again to basics – the Z7 and Z6 first version AF goes back to an era before advanced subject recognition became common - though they did have much faster electronic communication between lens and body than a DSLR, allowing several image corrections such as distortion to be made in camera, much brighter viewfinders etc, and with the wider lens throat and shorter lens flange to sensor distance often significantly higher resolution lenses became possible.
Limitations of early Mirrorless included being only able to recognise detail parallel to the short side of the frame, whereas DSLR's had some or all more effective cross type sensors.
Recent ML cameras have the ability to recognise a human body, a face, an eye, a bird, a car, an aircraft et cetera that neither DSLR or early Mirrorless could do.
The Nikon Z8 and Z9 have an extremely good subject detection system - and the Z6 III is almost as good - at a moderately lower price point than the heavier (a potential issue for you) Z8. If advanced AF ability is important to you this I think should be your front runner.
The Z7 II is good at AF for portrait, landscapes et cetera with face and eye detection but otherwise with a slower processor cannot match a Z6 III with advanced subject detection.
Although the Z7 II has the highest image resolution and AF good enough for most types of "traditional AF" photography - it is not a front runner for BIF etc that many subscribers to this forum undertake
The Zf is "interesting" - for those who hark back to the film era and want something like an old FM2 film camera body - and does this quite well. I suggest you rule this out for your needs.
What I cannot decide for you (only you can) is whether the lower priced higher resolution Z7 II or the much more advanced with potentially (depending on subject matter) more advanced AF is the best currently available choice for you.