Currently it's possible to specify mime types, but they don't actually do anything on the native side. We need to wire up an @available-gated path that uses allowedContentTypes instead of the deprecated-in-macOS-12 allowedFileTypes, and convert each filter type to its corresponding UTType. (The method channel already passes them separately, rather than combining them on the Dart side, to facilitate this change.)

(/cc @cbracken as this would be a good first "contribute to a macOS plugin" project for someone at some point.)