Odds are the new lens will be a lot more popular than the z8 was. The product works very well, and the price cannot be beat.
I doubt that is the case. There will be demand for the 180-600, but such long a lens is a niche product. And IMO the 180-600 will not be that useful without the AF from the Z9 or Z8 behind it. If more people own the 180-600 than the Z8, are they all Z9 owners?
The Sony 200-600 is one of the most popular birding and wildlife lenses today. You’ll find it on all bodies, from a6000 to the a1. I have an a1 + this lens, and I have a Z6 mk i, and a Z9, with a 180-600 on order. It won’t go on the z6, but that’s not to say I wouldn’t put it on a Z6/7ii or good APS-C body (a D500 replacement) if one comes along.
Your post highlights the situation for Sony as well as for Nikon. Sony's 200-600 is popular for birding and wildlife because Sony do not have as many super tele selections as Nikon have now. I have a Z9 also, and I have a 600mm/f4 AF-S VR and a 500mm/f5.6 PF in the F mount; I also have the 400mm/f4.5 and 800mm PF in the Z mount. Hence I don't have much interest in the 180-600.
On the other hand, Sony has more bodies with pretty good AF for action photography, besides the A1, there is also the A9 and even some APS-C bodies. For Nikon, if you get the 180-600 but do not pair it up with either the Z8 or Z9, it is kind of meaningless. Did you see the current thread that some Canon user wants to buy the 180-600 plus an inexpensive ~$1500 Nikon body with decent AF to go with it:
https://www.dpreview.com/forums/thread/4725376? Sadly, the simple answer is that no such "inexpensive" body exists today.
What Nikon will introduce in the future remains to be seen, but at this point, I seriously doubt that a niche lens such as the 180-600 will outsell the popular Z8, which is a very general-pupose camera. I am planning to get a Z8 also in the future; some people have multiple Z8s, but I don't see very many people with multiple 180-600 lenses.