HTTP Status Code 403 Forbidden can be used when a request isn't allowed based on the user's identification, so I guess it can be used in this case.
However, have you also considered sending back a Redirect (https://developer.mozilla.org/en-US/docs/Web/HTTP/Redirections) to send the user to a different resource that might be more appropriate because they are authenticated?
This is a common method used to redirect authenticated users away from login pages to their home screens or profile page.
Also, for future reference, I think you might be referring to autheNtication (with a N, the process of verifying a users identity) instead of authoriZation (with a Z, the process of determining whether an authenticated user has access to a particular resource)
https://www.okta.com/identity-101/authentication-vs-authorization/