Big Sur Mail Account creation fails: This account already exists

Running a MacBook since years without using a mail application. Instead, use web mail since years, including mail app on the iPhone.

Updated to Big Sur and want to use mail app. Added a Mail account for IMAP mailing, but it didn't work. 'Connection Doctor' was not able to fix it, so I removed this Mail account in 'Internet Accounts'.

While I use the same mail address for Apple ID I signed out, restarted the Mac, and tried several times to 'Add Mail account' via Mail app or directly via System Preferences - Internet Accounts.

Imagine what the error message is: 'This account already exists.'

How can this be fixed if Apple ID/iCloud signing out is not working? Thank you so much.