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I suggest to rename this parameter to copy_dir_stat:

1. The copystat in

   cpython/Lib/shutil.py

   Line 511 in cc39b19

   copystat(srcobj, dstname, follow_symlinks=not symlinks)

   is not affected.
2. The copy_function might still copy file permissions, e.g. the default copy2 will.

Perhaps copystat in this function (as well as other functions like copy2) could be replaced by copystat_function, similar to copy_function, thus allowing custom functions that can do some logging as well as propagating it to other functions. But at this point, there should be a class that can be instantiated with various hooks/overrides instead of multiple functions with way too many optional arguments that need manual propagation.

However, I really like to have such an option to override copystat, because globally overriding shutil.copystat = lambda source, *_ignored: source feels very wrong.