Hi again,
After some testing, it appears that the retrieved user profile cannot be modified through Auth0 directly. In order for the Management API to be able to modify user data, they would need to be stored via a Database Connection or Passwordless connection.
In order for your to update the user with such information, you either need to add these elements as user_metadata as you have attempted above or you would need to make an API call to the IdP in order to add these attributes to their profile so that they are retrieved after login (if the IdP can support them).
Sorry for the confusion created on this matter.
If you have any other questions, let me know!
Kind Regards,
Nik