Thank you kindly @ElenaH, and yes indeed, those old Nikon lenses like the 180 and 80-200 which I own produce something magical, no doubt about it. Images just seem to pop with them, great shame that Nikon don't offer a converter with built in focus motor for those.@Snapquacky , I've read almost all and would like to share my thoughts.
You wrote you have old screw-driver lenses from Nikon. I have 180/2.8, for exaple and I must say that there are no such lens like old Nikon screw-driver lens in terms of colour and overall rendering. Yes, they have horrible CA's and cannot focus on mirrorless but they give a special look : the saturated deep colours, sharpness (oh, yes, they are sharp) and some kind of 3D-effect.
So, 800PF is closer to those lenses than 200-600 of Sony. My partner has Sony A7R IV and 200-600 and Z9+800PF. After he has got 800PF, he doesn't use Sony anymore. Moreover, he has 400mm/2.8 FL (F-mount excellent lens) which he used with TCs and now he doesn't use it anymore, too. What is good for me ;-) becasue I can use it. Bur 800PF focuses much better/faster on Z9 than Z9+400FL and I think that Z9+800PF is overall better than Z9+400FL+2xTC. So, 800PF is amazing lens.
So, what I want to say is that you'd think what you like more: the look of pictures shoot by Sony or Nikon. Let's say you will buy Sony and don't like the pictures (the bokeh of 200-600 is so "olalala...," for example), than you spent your money and perhaps, you are not unhappy but don't have so much joy and fun like you would with 800PF (what I can guarantee - you will have a LOT of joy)
Perhaps you should rent both combilation and try.
The other thoughts are about Z7 vs Z6. If you take pictures of birds than normally there is already light or there is a short period of dusk. Normally. the birds sleep at night (ok, if you will take pictures of owls than it is different). And there is an excellent software to reduce the noise. I think, the noise will not be an issue but more pixel is better.
If your ever want to take part on some photo-contest then you need a high-resolution camera. The requirements for picture-resolution for contests are very high. So, I would go for Z7. If you additionally do some other kind of photography like astro or nightscapes then Z6 will be better.
I understand the A7R IV and 200-600 don't always play together so well in certain situations, but it is great to get real world feedback from someone who has access to both setups. Between the three lenses you refenced above you have a great selection there! not bad at all. Your feedback on the 800PF is most useful, sounds like it is getting back to the Nikon magic recipe for glass.
Mostly I use DXO for noise processing, it works amazingly well, very impressive. I do end up in low light quite often, so in some respects a lower resolution sensor like Z6 would work well, but I am keen to go above 40MP for cropping and downsizing to mitigate noise.
Please post some images from the 800PF if you can, or any images for that matter, always a pleasure to view wildlife