It seems that I've solved this issue.
I managed to contact Apple via their "feedback assistant" website and in almost 6 months we found a solution.
They never said this clearly to me, but it seems that iOS 15 is more strict about DAV flows and, maybe, is making some unneeded anonymous calls...
In my case, my server had those 2 behaviors that iOS 15 doesn't like:
replying 403 forbidden to anonymous requests instead of 401 unauthorized
including a 418 empty entity in some PROPFIND requests
Solving these issues made iOS 15 CalDAV client work again