You know, the A7RIII is a perfectly good camera at 42MP, and I know from my d850 experience that can work well for birds and action. The A7RIII will do 76 continuous exposures @ 10FPS (I only get 9FPS on the d850) with raw. from what I understand, it got a big AF boost the last firmware update too. And you'll find a lot of used ones now and get a deal, or take advantage of the Sony $500 savings on a new one.
I understand it's not as sexy as an A9 or A7RIV, but I know it will give good results. 42MP will get diffraction limited beyond f/8, but f/8 is good for fastish lenses (like the 500mm f/5.6 or the 400/2.8 + 2x TC options) and gives quite a bit more DoF.
To use my previous calculations:
24MP: 400mm * 2x (tc) * 1.55 = 1240mm @ 10MP or 1736mm @ 5MP
42MP: 400mm * 2x (tc) * 2.05 = 1640mm @ 10MP or 2296mm @ 5MP
61MP: 400mm * 2x (tc) * 2.47 = 1976mm @ 10MP or 2766mm @ 5MP
The other thing to think about DoF is this. The A7RIII has a pixel pitch of 4.5 um and the A7RIV has 3.7um. What that means is you lose about 1 stop of DoF on the A7RIV -- a smaller airy disc will cause the same DoF blur as a larger disc on the A7RIII. The A9 is about 6um.
One way to think about this, is one usually needs the defocus blur to be < 2x pixel pitch (
George Douvos). The A7RII (and d850) can take a blur of about 9um and the A7RIV of about 7um. The Sony A9 can take around 12um.
Here's some example numbers. To extrapolate to longer distances, it goes more or less as the square (e.g. 0.14m @ 10m ~ 14m @ 100m).
Code:
A9 : 400/2.8 x2 at 10m is 0.020m DoF, at 20m is 0.08m, at 40m is 0.33m
A7RIII: 400/2.8 x2 at 10m is 0.017m DoF, at 20m is 0.07m, at 40m is 0.27m
A7RIV : 400/2.8 x2 at 10m is 0.012m DoF, at 20m is 0.05m, at 40m is 0.20m
The same thing at f/8:
Code:
A9 : 400/4 x2 at 10m is 0.030m DoF, at 20m is 0.12m, at 40m is 0.47m
A7RIII: 400/4 x2 at 10m is 0.020m DoF, at 20m is 0.09m, at 40m is 0.38m
A7RIV : 400/4 x2 at 10m is 0.017m DoF, at 20m is 0.07m, at 40m is 0.28m
So without getting into diffraction limitations, you will have a pretty shallow DoF at mid-range distances for the A7RIV at 800mm (10-20m), especially compared to the A9.
Lloyd Chambers puts it like this: compared to the A7RII you should stop down 1 stop more for similar DoF, but to avoid diffraction you want to stop down 1 stop less. Basically, you are squeezed from both sides.
So in summary, the A7RIV will let you crop about 1.6x more, but you also have about 1 stop more DoF blur unless you start getting diffraction limited beyond f/5.6. I think it's going to be a pretty small operational window for the the 61MP sensor, especially for larger birds that you might want to try and get mostly in focus and thus need f/8 or f/11 -- you might lose that to diffraction especially if cropping heavily.
I go into all this detail because your goal is to improve image quality with very long focal lengths (800mm) and heavy cropping. Unfortunately, more MP is not always better, but if you can shoot the A7RIV in the goldilocks zone it should give stunning images.
Marc