If you are accessing your @eng.ucsd.edu Google account in any way on your phone or tablet - you will need to remove the @eng.ucsd.edu account from your phone, and add the @ucsd.edu account instead, once you're up and running with the @ucsd.edu account.
Once your @eng.ucsd.edu account has been renamed to archive-username@eng.ucsd.edu, your phone will prompt you to reauthenticate. You have the choice to keep your archive @eng account on your phone for the time being, or you can remove it right away using the info in the links below.
Remove account on Android phone:
https://support.google.com/android/answer/7664951
Add account on Android:
https://support.google.com/android/answer/7664951
Remove account on iPhone:
https://support.apple.com/guide/iphone/add-and-remove-email-accounts-iph44d1ae58a/ios
Add account on iPhone:
https://guidebooks.google.com/iphone/setup/how-to-sign-in-to-google-account-iphone - Note that instead of the Google password page, you'll be redirected to Campus Single-Sign On, where you can sign in with your Active Directory Username and Password.