Transferring to a new Mac does not require creating an entirely new apple Account. You should have been able to sign in with an exiting Apple Account just fine. In fact Apple recommends keeping one Apple account only updated and accessible always. Creating new account is not something Apple ever suggests you do.
Your email is not tied your Apple account except for iCloud email. So not sure what you mean by connected email accounts.
Seems to me you misinterpreted something and now are just making more odd decisions you should not need to be making based on faulty information.
If you explain exactly what happened, someone may be able to help you resolve it. \
As it stands, it would be better to just sign of the new account and log in with our old existing one to keep access to all content, subscriptions and apps that are and will remain tied to the old one.