Thank you for providing the additional details!
As you want to disable the sign up option for your users on the login page, this can be done on a Database level by going to the Settings page of the Database ( in your Auth0 tenant ) and enabling the " Disable Sign Ups " option. You can read through our Disable Signups at Connection Level article and in case you want to disable Sign up on the application level, I can recommend our Disable Sign-ups for a Specific Application documentation.
For added details, I can also share our Don’t show “Sign Up” option on New Universal Login topic that mentions how to handle Social Connections in this scenario, if it suits your extended use-case.
Have a great one!
Gerald