New mails don't appear in Inbox

Twice new mails have stopped appearing in my MacMini mail Inbox. I get notification that a mail has arrived, but it's not in the Inbox. New mails do appear on my iPhone and iPad, and in my linked Outlook account. The first time this happened, I >Rebuild, and the next day all the mails were there (BUT with all flagged mail moved to "Flagged"). Today, a few days later, again new mails stopped appearing, and older ones disappeared back to 7/7/23. This time, I called Apple Support. The first agent was puzzled, and Apple Support cut out mid-call. The second agent poked around the mail app, and suddenly some new mails appeared - BUT not all of them. Also the test mails I sent at their request no longer had the BCC field, even though it is set to automatic in Settings > Composing. I would appreciate any insight into what might be causing this behaviour.

I am running Ventura 13.5 on a new (January 2023) MacMini. I get my mail through an Exchange account managed by Stanford University.