Here’s my take. All of the cameras you have looked at should be more than capable of shooting pretty much anything, whether it be the A7III, A7IV, A9, A9II or A1, all have incredible AF systems and one is not revolutionary over the other, they are incremental steps. Lets remember, the D750 was the go to wedding camera for a lot of people a while ago and these cameras will beat that hands down.
In terms of eye-AF the A7IV may well be better than the A9II however I’ve found more often than not the A9II picks up the eye of birds, even small ones such as tits and robins, assuming they are not teeny tiny in the frame of course. If I was deciding for me it would be a case of do I want the separate drive/AF dial and blackout free shooting, or do I want that extra 6mp resoltuion. If it’s the former get the A9II, if it’s the latter get the A7IV. I’m personally not that convinced 30mp over 24mp is that big a deal in the real world, YMMV.
If you want it all then get the A1