Thanks for outlining the options, @Dominik Hoefling! Other than enabling verbose logging in Outlook (which slows Outlook), I have done the other 2, but have not gotten the information on IMAP detailed events logging. I saw that the account connected via IMAP, but I did not see if the Inbox folder was downloaded, or emails were synced.
No, I was not able to figure out the POP/IMAP activities in a mailbox. When I was investigating this, logging POP/IMAP activities was available for on premise Exchange servers, not with Exchange Online.