I see you have a D500 in addition to your Z9. The 500 mm PF will work with both your Z9 and D500. The new Z 400 mm f4.5 will work only with the Z9, if that matters.
I have spent some time considering the Z 400 mm f4.5. I have a Z9, Z7II and Z6II. Still have my D850 and D500, but should sell them, as I have not used them since getting the Z9. I think the choice between the Z 400 mm f4.5 and the 500 mm PF turns on the factors Eric mentioned and also on what other lenses you have or plan to get and what and where you shoot.
I have the Z 100-400 mm and the 500 mm PF. The Z 100-400 is valuable to me for its zoom flexibility and close minimum focus difference. It is good at 400 mm, but, of course, not as good there as the Z 400 mm f4.5. If I were to get the Z 400 mm f4.5, I’d also keep the Z 100-400 mm.
Since I have a competent choice at 400 mm, for me the need is for something longer. I photograph a lot of birds, both large and small. So I would probably generally be using the Z 400 mm f4.5 with the Z 1.4x TC (or maybe even the Z 2x TC). Once you do this, it is not faster than the 500 mm PF, as the TC makes turns the Z 400 mm f4.5 into a 560 mm f6.3 lens (or 800 mm f9 with the Z 2xTC). So with Z 1.4x TC, a third of a stop slower, but 12% more focal length. I could see either way as a reasonable choice and I am sure that the optical quality with a 1.4x TC is also very good either way, with differences not very relevant in day-to-day wildlife work.
With a 1.4x TCIII, the 500 mm PF is 700 mm f8, so 140 mm more focal length than the Z 400 mm f4.5 with the Z 1.4x TC, but 2/3s of a stop slower. Of course, if you want 800 mm, you could use the 1.7x TCII on the 500 mm PF (leaving you with 850 mm at f9.5) or the Z 2x TC with the Z 400 mm f4.5 (leaving you at f9).
I have found the 500 mm PF with the 1.4x TCIII (and even the 1.7x TCII and 2x TCIII) to be quite useful on a Z body, particularly the Z9. I bought the 2x TCIII for my 500 mm PF on a Z body after Brad Hill said he found it quite useful on a Z body. You might find Brad’s discussion on his website of using TCs with his 500 mm PF useful.
It’s possible that I would make a different choice if I did not already own the 500 mm PF. It is also possible that my thinking will change, as I pick up my 800 mm PF early next week, so I will be using the 800 mm PF in most cases rather than the 500 mm PF with a TC.
I do see the Z 400 mm f4.5 and a 70-200 f2.8 (in F or Z mount) as a very good low light kit, if 400 mm is enough focal length. And the Z 70-200 mm f2.8 (which I have) is a very good 90-280 mm f4 lens with the Z 1.4x TC.
Thom Hogan has an interesting short discussion of the long telephoto choices available for Z mount photographers.
https://www.zsystemuser.com/nikon-z-system-news-and/telephoto-options-round-two.html
Good luck with your choice. As Eric notes, hard to go wrong with either lens.