Well, I sort of figured out and solved my issue. Doesn’t explain it, and doesn’t explain what change there was that created the issue, but nonetheless here’s it is.

On the setup for AOL mail by IMAP, they provide a default set of folders: Inbox, Draft, Sent, Trash, Bulk, Archive, Drafts, Notes, Saved, Spam. When you add an AOL IMAP mail account to Outlook those folders show up.

Well, some time ago, I created a subfolder within the INBOX (nested, as it were) and created a rule such that mail from a certain group of people would end up there. I created this subfolder in Outlook, and this synchronized back to the AOL server. It functioned without issue for some time. Note, I also have the same setup on another email Inbox (Exchange, not IMAP) and a second Inbox (POP3, not IMAP) and these have worked perfectly for years, all on the same Outlook 2011 for Mac. The subfolder for the AOL account worked fine until July 25. At that point, nothing synced on the INBOX side, but it did take me some days to notice that. Most of my mail is initially read on the iPhone, and the problem did NOT manifest itself there, nor on AOL webmail, nor on Outlook for iOS. Just on the desktop version.

So, just out of curiosity today, I went to webmail on aol.com, moved all the messages in the Inbox subfolder back up into the Inbox parent, then deleted the subfolder. Now, only one Inbox, no nested subfolders.

...and that solved the problem. All the mail started syncing and function is back to normal. For some reason, the AOL IMAP setup on Outlook can no longer handle nested folders in an Inbox, as of July 25. Why? That I cannot tell you.