this thread has two topics - 1. duplicate notifications (probably due to imap folder subscriptions) and 2. unexpected authentication behaviour. They could be connected, but do not need to be.
As to 2., I’m seeing fixes end of July and August down the oauth/sso/mail alley at Commits · main · e / os / AccountManager · GitLab - if a user wants to side-step this until ironed out, use thunderbird mail / k9 and davx5.
Imo what 2. experiences is a consequence of Murena trying to make single sign on and first-time on-device authentication setup for all Apps work. Though it’s hard to do so without introducing bugs with a missing test harness covering both accountmanager and mail.