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I'm not a security guy, but: shouldn't the os.unlink call when it isn't a directory specify follow_symlinks=False? And wouldn't it be safer if the os.rmdir() call also used dir_fd=?
Additionally, I think you missed some stuff for shutil._use_fd_functions. Assuming I'm right on both of the above, you should also check:
* os.listdir in os.supports_dir_fd
* os.rmdir in os.supports_dir_fd
* os.stat in os.supports_dir_fd
* os.stat in os.supports_follow_symlinks
* os.unlink in os.supports_follow_symlinks
I'd spell that
_use_fd_functions = ({os.listdir, os.open, os.rmdir, os.stat, os.unlink} < 
 os.supports_dir_fd and
 {os.stat, os.unlink} <= os.supports_follow_symlinks)
Finally, up to you, but I'd be tempted to change the "lstat" "and "fstat" calls to "stat" calls using the relevant parameters.