Given the sensor used, is it likely to show up in the Z6iii ? I doubt it though, as consensus seems to be that it’s a premium option, for the time being.
I think the price difference between Z6 series and A9 III is too high - in my opinion, the 1500-3000€ price class is critical as there are a lot of enthusiasts and professionals that can afford and do use cameras in this price class. The A9 III would seem to be a specialist's camera for fast action and pushing the edge of what is possible rather than a general-purpose camera like the Z6 series.
Now, whether Nikon would make a Z8H or Z9H model with 24 MP global shutter sensor, that's always a possibility, but it seems Sony and Nikon, although they are partners in some areas, they're also competitors and don't seem to use the same sensors in most of their cameras these days. I guess there are some things they share and other things they keep from each other where it comes to technology development.
Normally one would expect the GS to lead to an image quality hit, as fast sensors generally do not have as low read noise as the slower ones, and this together with the high cost may put off manufacturers from placing this technology in more mainstream models.
There are previous GS cameras for video applications, such as the Canon C700 GS PL, but the cost is high and DR takes a hit.