Hi,
Currently, the New Universal Login Experience does not support Additional Sign Up Fields. However, still you can use the Classic Experience with Lock SDK to show additional Sign Up fields.
To learn more about Custom Sign Up, please refer to: https://auth0.com/docs/libraries/custom-signup and Lock Configuration Options.
After capturing the required data, you can save them in the user_metadata in user profile. Then, you can add them to the user’s Access Token via a Rule (Read more: Sample Use Cases: Scopes and Claims)
I would also recommend you to research more into Role-Based Access Control. Generally, we do not allow the user to select their own role and Identity Administrator should set them up for the user.
Hope the above information helps. Let us know if you have further questions!