IMHO I would go with the D850. I got mine some time ago and, loved it from moment one and still do it ... AND got rid of my DX body (D7200 at this time). Sounds weird ? Well, here's why:
When I struggled with the decision to spend the money I ended up asking
@Steve about it and he confirmed that the D850 has "a D7200 built into it", and I would expect it to be the same for the D7500. BTW I preferred to have the D7200 at the time because among some other advantages it could take a grip.
- If you shoot the D850 in DX mode you get 19,5 MPixel versus 20,9 for the D7500 and 20,7 for the D500. That means you are loosing just 7% against the D7500 and 6% against the D500. Also the D850 has the same generation processing electronics as the D500 (Expeed 5)
- The AF sensor coverage of the D850 in DX mode is better than native D7200 (as well as the D7500 I would expect)
- With the grip you have a bit more weight, bit it gives you 9 fps which should be plenty for what you wanna do.
- Looking at lowlight performance the pixel size is still the most important factor. The D7500 has 17,8 µm², the 18,92. COmbined with the newer electronics and software the D850 in DX mode will easliy at least keep up is not outperform the D7500 (as well as it did with my D7200) in terms of low light noise. I know that many people out there argue that in times of AI denoising this is not a big issue anymore, but in reality it still is, because despite all modern tools it is still best to get maximum IQ in the first place and then just use those tools to push the limits.
The D850 can do everything that your D7500 can do - and even better, so if I were you I would just swap the D7500 for a D850.
Regarding lenses I can confirm most of what has been said before. If you are not in the position of carrying heavy guns to stationary observation stations, but you want to be light and agile, the 500PF if proably the best you can get for birding. IMHO the only disadvantage of it is the price you have to pay for the extreme mobility this lens provides, and that is the f5.6. Hardore fans of object isolation like
@Steve prefer the heavy guns for exactly this reason. But another argument is that the use of a TC-14Ex on the 500PF is limited - at least for what you want to do, because you go down to a f8 lens and this will make most most of your AF sensors sitting around doing nothing, i.e. of the 153 (99 of which are cross-type) you just keep 15 working if using a 500PF with a TC-14x.
A gripped D850 with a 500PF is so nicely balanced, that for me it is almost on par with one of my older "naked" bodies combined with the 24-70 f2.8E on it. And because it is so nicely balanced I have also made good experience with using travel an landscape tripod with just a 30mm ball head (Feisol CT-3441 with CB-30D) if I really want to or have to go light. The combo is very light and stable at the same time and this experience made me think of going one step further and swap the ball head against a Flexshooter Mini. As a result my big Gitzo would be primarily used for the the heavy combo (500 f4 + TC14 ).
Good luck with your decision
.