That is a really odd response to the test email. Apparently your email SMTP server is allowing you to relay emails to the email address you have in your admin notification field, but NOT allowing relay to any external emails otherwise.
Authentication failed means that the email SMTP server you are using requires a username and password in order to relay those emails. That is typically the email address and password you need when you log directly into their email service. You should have that info available, but if not, you need to contact the email service provider you are trying to use for the SMTP relay service, and coordinate getting the right credentials with them.
Once you have created another super admin, you can manually set a password on any accoount so you can regain the other account, regardless of the email functionality.