Unable to log in to business account with Apple ID due to private relay conflict

I opened an account for a business using my Apple ID.

the business thinks my private relay is my regular email account & after I logged out of the account I can’t log back in. When it ask for two step verification it only recognizes the private relay & therefore I never receive a code. The business stated I would need to open a new account using my email not the private relay. I have a refund coming but they stated the only email there system recognizes is the private relay & they can’t do anything about fixing it. Any suggestions

[Re-Titled by Moderator]

Original Title: Private relay