Can't move messages from Inbox to folders.

Yes, the Mail program was probably trying to synchronize with the (failing) IMAP server. But instead of just waiting for the server, it was moving mail messages back to the Inbox. This is what was so bizarre. It should show the correct disposition of the messages on the machine where I moved the messages; and the server and any other machines might take a while to catch up, and in the meantime would show the messages as still in the Inbox. If the problem with the server persists, there should be some kind of error message like "Cannot synchronize with IMAP server." But the messages should stay where I put them. Most likely this bug was introduced in some recent MacOS update and this is the first time that the Verizon server has failed since that update. (The Verizon email servers are notoriously unreliable. They go offline for hours at a time about once every month or two.)

I select one or more messages, and then drag them to the desired folder. They disappear from the Inbox, as if they are being moved. (And the incredibly slow "Moving Messages" status appears in the lower left.) Then, after a few seconds, those messages reappear in the Inbox. This has always worked before, literally for years. Also, another bizarre new behavior is that if I right-click on a folder and select "New Mailbox", enter a mailbox name and press "return", it now takes two or three tries. It just ignores the "New Mailbox" request the first one or two times. No error message or anything, it just ignores the request. This is MacOS Monterey 12.3.1 and Mail Version 16.0 (3696.80.82.1.1).

A.1 Whatever the previous version was. I have always been applying the updates when available. I don't keep a spreadsheet of every one of thousands of Apple versions.

A.2 Very few, if any, have any attachments at all. They are just simple email messages.

A.3 It is a Verizon email account. But the Mail program downloads the messages onto my computer, so the server is not involved in moving from one folder to another.

A.4 It is using IMAP; however, as I said in answer to your answer A.3, the mail messages are on my computer, and the server is not involved in moving them from one folder to another.

A.5 I have not tried this using webmail. But whether or not it works there is not relevant to any bugs in the Mail application.

I tried again moving some messages by right-clicking and finding the folders on the pop-up menus. That appeared to work. Then I tried clicking-and-dragging again, and now that works. So possibly moving the messages by right-clicking etc. reset something that had been messed up. I don't know if a couple of hours waiting fixed the problem, right-clicking fixed the problem, or if it the problem just went away for some other unknown reason.

So I have no confidence whatsoever that this bizarre behavior won't recur, since I have no idea why it would do something like that in the first place, and I probably did not do anything that was likely to fix the problem.

Thanks for your help.