The horizon is not level, but that didn't bother me much. However, this is very easy to fix in programs such as Lightroom. The highlights do look blown a bit.
With a 5.6 lens on my crop sensor, I rarely need to stop down; I suspect the same is true on your Z9. You've generally got plenty of DOF; for this shot the bird is far enough away that 5.6 would have been better. You might want to play with a DOF calculator for 5.6 aperture and 500mm focal length at various distances to get a feel for how much DOF you really have with that setup. (Note: everybody gets caught out sometimes with the right settings for the last shot, and not this one which is what happened with you it seems .... )
1250 is slow for BIF, that said, looking closely at the eyes, I don't think sharpness is bad; faster would have been better. I think the background is not great (it's annoying how often birds refuse to give me a nice background) though shooting at 5.6 would have helped a little.
If I was post-processing this in LR I'd attempt to make the background nicer. Steve has a nice video out on using Adobe AI denoise to, well, denoise, but as part of that workflow he also likes to mask the background and soften it (look for the video) by reducing sharpness and texture along with using the basic denoise in the mask. While masking the background I'd probably desature it just a bit, because the background colors do not make me happy. Here I'd also mask on the subject to try and get more detail in it (less highlights, more texture and clarity, etc).
Finally, again if you are using LR, I'd experiment with the lens blur tool; results vary quite a bit but if the subject is in a very different focal plane than the background, it can sometimes clean things up a lot; this picture definitely looks like candidate for trying that tool.
Some of the suggestions are LR specific, but most tools should allow you to level, mask on just the background and soften it, etc.
I assume you were in burst mode and this was your favorite composition from the burst. For a situation like this, I'd capture at least 10 shots in the burst, probably more.
This shot is okay given the conditions and subject. Better light and a wider aperture (for a softer background) with faster shutter speed are the main things I'd want different at the time the shot was taken. The only fix for better light is being there at a different time, of course. Can you verify for us what time the picture was actually taken?