I like the swallow in particular, great shot, Alan. I know how hard it is to catch a swallow in flight. The other BiF images are more from the backside, so the AF already had a relatively long time to get the bird in focus. I personally prefer more images of birds approaching or passing exactly by, so the AF has not that much time to focus on. What definitely helps is switching off eye detection, maybe simply because the R7's processor has to process less data.
I am not sure whether my R7 in particular struggles with with the EF 600mm III, I had the same problems with my old EF 500mm f/4.5 - okay, that's a vintage lens - but also with my RF 200-800mm the R7 doesn't perform always well when I try to shoot against some skies. Interestingly, the Nikons of my wife display the same behavior in some special light conditions, we asked ourselves already if this could be caused by polarization effects (she is a physicist, too). I should start taking notes about these settings. But when I am shooting birds I don't want to distract myself. Well, when I want more reliability, I take my R5 II, like in the DSLR times, when I switched from my 7D's to my 5D3/4 to have a better AF performance.