I agree the naming is a mess. There is the Australian Digital ID system (https://www.digitalidsystem.gov.au/how-the-system-works) which allows third party providers.

Whatever the capabilities of the Australian government ID services, there is a way to issue privacy-preserving tokens that could do all the things you'd need without being trackable the system was properly designed. (I have not studied the protocols of the Digital ID spec to say whether that's the case).