I hope it works out so you don't feel as if your older lenses aren't reliable. A lot of photographers with expensive, legacy glass would hold off moving to mirrorless.The percentage of subjects in focus is about half of the shots , if the background is plain colured. If there is some "troubled background" like trees, grass, e.g., it drops to one quarter or less. This is just feeled, not counted.
Today, the service center wrote, they will check my R5 and the lenses. Canon recommends for good AF performance using Rf lenses - or with the long telephoto lenses Mark III versions. (600 III and 400 III).
I wonder how the older lenses are working on the ef 1DXIII? What would it be specifically about the mirrorless AF system that doesn't work as well with the older glass?
Have you tried using a slower burst rate just to see if the lens needs time to keep up with the R5's focus system? That's just a brainstorm idea.