Problems with client mail.app and mail on iCloud.com

Running mail.app 16.0 on a MacBook Pro 16 inch 2019 under macOS Monterey Version 12.4.

All of a sudden today my ****@mac.com and ****@icloud.com mail is completely crazy. I’m getting all sorts of messages about not being able to move email to iCloud and mail that does come into these addresses won’t load in the mail.app viewer. At the bottom of my list of mailboxes I see messages about mail being copied or moved. Sometimes while trying to respond to a message a box will pop up that says

The message “test from iCloud.com to .art” could not be moved to the mailbox “iCloud” Mail was unable to open this mailbox on the server “p64-imap.mail.me.com”. The server returned the error: Server Busy. Please try again later. (took 0 ms)

What’s really even more baffling is that if I go to iCloud.com, sign in and click on the mail app, the interface comes up but there’s a spinning cog wheel for a while. Earlier today after the wheel stopped spinning, I’d get a message that said something like there was an error and mail couldn’t be opened, try again later. I just a couple of minutes ago went to iCloud.com again and clicked on mail and got the spinning cog wheel again, but this time no error message and I’m able to see a list of my messages on the left. However, when I click on one to read it, the email opens, but I just see its subject. Eventually, after several minutes, the body of the email will appear.

Does anyone have any idea of why this might be happening and what I might be able to do about it? I’ve never seen anything like this before and am totally at a loss, especially because it’s not only the client mail.app that’s messed up but the mail app in iCloud itself.

TIA

[Email Edited by Moderator]