Unfortunately the issue appears to be that Google insist on your new Gmail address being the primary and that is what is made available when using Google to login.
See here for information on the Gmail username restriction: Change your username
Assuming this is the case and the connected site relies on your email but can only access the new Gmail one then the only option I've been able to find at the moment is to remove Gmail from your account and go back to using your previous username/email.
You can do this by following these instructions: Canceling your Gmail address
I've just done this myself so I could log back into Stack to post this response so it does work as long as you don't mind sacrificing the Gmail username. You can always create a new separate account for Gmail but according to the link above:
Deleting your address won’t free up your username. Once you
delete your Gmail address, you won’t be able to use that same username
(firstname.lastname@example.org) in the future.