The 500 mm PF + 1.4x TCIII + FTZ or FTZII works very well on Z bodies. Better, in my experience, than on a DSLR (at least my D500 and D850). I have used mine on a Z9, Z7II, Z7 and Z6II. The combo works particularly well on the Z9.
There are several reasons why it works better on a Z body: All the focus points work across the frame, even though the lens/TC combo is f8. On a DSLR, only a small number (8 or 9) of the focus points near the center of the frame work with an f8 lens or combo. Also, there is generally no need to focus tune the lens + TC, something that is often needed with a DSLR even if the bare lens does not need tuning. I also find that the 1.7x TCII and 2x TCIII work well with the 500 mm PF, an FTZ or FTZII and the Z9. If you have the choice, the FTZII works better with the Z9 than the original FTZ, given the built-in vertical grip.