As posted above, the body it's mounted to matters and in some cases even the battery used can matter. For instance I find my D850 with the optional vertical grip focuses my 600mm f/4 noticeably faster with the larger higher voltage battery installed rather than the stock battery. But yeah, choice of camera can impact focusing speed.
And as posted above a BIF coming straight at you is one of the most challenging tasks (next to birds with really erratic flight patterns like Swallows and Fly Catchers). The only time I get reliable shots of birds heading straight towards me is when I acquire focus early when they're still far away and keep focusing while I track them in until they're large enough in the viewfinder to begin releasing the shutter. One other trick is to pre-focus at about the distance where I think I'll acquire another incoming bird by quickly focusing on a bush or other object near that same distance to get ready for the next bird. This obviously works best when there's a typical approach pattern to your location like birds flying into the wind to land in a watering hole.