I performed a manual mail check for the account in question and then successfully proceeded to change it to OAUTH2 authentication.
About 2 hours before attempting to change the account to OAUTH2 authentication AquaMail performed a scheduled sync in the background. So I incorrectly assumed the FAQ "Version 1.5.1+: Google's new authentication, OAUTH2" instructions had been satisfied:
First, make sure that the app has checked mail in this account at least once, so it can detect that it’s a Gmail (or Google Apps) account.
Second, long press the account, choose Account setup, and you should see a green panel with a prompt to upgrade. Once an account has been switched from login / password to OAUTH2, there is no going back, so might make sense to create backup first (Menu -> Backup & Restore in the account list).
And yes, I did do a Backup before making these changes.
Thanks for the help Kostya!
PS I think my problem was caused by installing AquaMail version 1.5.1.6 after the scheduled sync was done.