On filesystems that support the features: in the file system itself. On filesystems that don't support the features: somewhere on the system itself (like in the registry on Windows) or not at all (for example, when trying to set permissions on FAT32). Other operating systems generally don't create hidden files for this reason.
They do, however, create their own versions of the recycle bin/trash folder. If you use a flash drive on macOS, Windows and some Linux environments, you'll end up with three different recycle bin/trash folders. A bit annoying, but those folders are usually empty anyway.
Windows warns about the inability to copy permissions to FAT32 (in some cases, at least) and some command line tools on Linux do as well, but it depends on the tool.
It would be nice if Linux at least could see the Recycle or Trash folder and use what’s already there. Even better if both macos and Windows started doing the same.