mail not coming into Inbox

Twice it has happened that new mails have stopped appearing in the Apple Mail Inbox. The new mails do appear on my iPhone and iPad, and in a linked Outlook account, just not on the MacMini. The first time this happened, I >Rebuild, and the next morning, all the mails were there (but all the flagged mails had been removed from the Inbox and put into the Flagged box). The second time, today, I called Apple Support. The first agent took over the screen, was very puzzled, and then Apple Support broke off in mid-call. I called again, the new agent looked around the screen, and suddenly some new mails appeared, BUT not all of them - there were new mails in Outlook that didn't appear in the Mac mail Inbox. As well, even though I have set the system to automatically BCC me, now none of the mails I send have the BCC. I am finding Apple Mail to be very unreliable.

I am running Ventura 13.5 on a new (January 2023) MacMini M2, and I use an Exchange account through Stanford University. Could my use of the Exchange account have anything to do with this behaviour?