Do you mean that you have SSO with one particular institution (e.g., whatever.edu) and you want people to stop using that email address?
There isn’t any way to trigger emails to an institutional account (other than an email validation request) in any scenario.
Isn’t the best way to keep people from impersonating someone to require them to use their instutional email address? There’s nothing to stop anyone from creating albert.einstein123@gmail.com and look like they are that person.