Summary: WP Mailster is currently not able to connect to Microsoft 365 (Office 365 / Outlook Online) and Google Mail (GMail / Google Workplace / GSuite) email servers since the companies are no longer supporting password-based email authentication for email applications.
Background
Google and Microsoft announced in 2021 and 2022 that they would stop supporting password-based authentication and require applications to switch to the OAuth 2.0 authentication standard.
Microsoft: Deprecation of Basic authentication in Exchange Online
Google: Transition from less secure apps to OAuth
Why WP Mailster does not support OAuth (yet)
WP Mailster, like hundreds of other PHP email solutions, uses the standard PHP IMAP library (https://www.php.net/manual/en/book.imap.php) in order to connect to email inboxes.
As of today, the standard library does not support OAuth.
Unfortunately, there is no sign that the PHP team is working on this. They identified the missing OAuth support as a problem back in 2019/2020 and put up this page: https://wiki.php.net/todo/ext/imap/xoauth2 and opened a tracker item (https://bugs.php.net/bug.php?id=64039) with almost no activity.
Due to this unfortunate situation, alternative libraries have been proposed. However, they either are completely different from the PHP IMAP library, or the libraries are very new (only months old, i.e. not battle-tested with a lot of different email servers).
That means, if WP Mailster has to switch to an alternative PHP IMAP library, it would go from a piece of software that was nurtured for over 10 years, with many learnings along the way, to something sparsely tested.
Hence, we are currently investigating the best course of action.
While it is currently not working: we intend to support OAuth 2.0 in the future.