Sony a9ii vs Canon R6 mark ii - Sports?

Which camera would be best for shooting sports (baseball and basketball)?

I plan to pair whichever body with a 70-200 f/2.8. I have also toyed with the idea of saving and getting the Sony 50-150. Eventually I’d also like to add a 100-400/500 to my kit to give a little reach.

Which camera has the best autofocus?

Is rolling shutter better on either one? Is that something I really need to be concerned about?

Are there other things/cameras that should be considered?

(1) Budget, country, and currency: Approximalty $4500 USD (body+lens). I plan on buying used to keep costs reasonable.

(2) What equipment, if any, you have now and why is it no longer meeting your needs? I don’t have any equipment for Sony or Canon. I currently have an X-T5, but the autofocus hasn’t been sticky enough. I plan on keeping the Fuji for most other needs.

(3) What kinds of subjects do you intend to shoot? Primarily my kids sports (baseball and basketball).

(4) Is it primarily for photography, videography, or both? Strictly photography.

Thanks for the help.