A play-by-play, as requested:
Apple Mail stopped being able to download POP email from my personal domain after a reboot last night, but I did not realize the problem until this morning. After another reboot and repeated efforts to try reentering the password, I contacted my domain host in a chat, and they suggested a number of alternatives including just using webmail (which I detest), and deleting the account and re-entering the information for it in a new account on the Mac. Knowing that that would zap any mail left in the InBox, I signed off the chat to sort out what to do.
In addition to my personal domain, I have three accounts managed by gmail (two on Google and one for a third party that uses Google), an iCloud account, and one at Verizon (largely unused). I manage them all from my MacMini (not the Air, which I clicked by mistake). The list of accounts also included one former hosting company that went out of business. That made it complex to manage the accounts. All but the personal domain are IMAP, but my contract with the hosting company does not give me enough storage for IMAP so it is POP.
My standard procedure is to move mail into an OnMyMac mailbox to preserve it every year, so I did that with the Mail in my personal domain account, creating "Inbox 2021" in On my Mac. Then I cleaned out the obvious cruft in the list of accounts -- forgetting to move the SENT mail from that domain to an OnMyMac account.
I called my host company, gave the tech on the phone my information, and he supplied the set-up information I needed to create a new account. That worked, and for a little while I thought I had solved the problem. Then I realized the mail I had sent from that account was gone, and turned to Time Machine to recover the whole Sent Mail box, which includes several accounts. I went back a couple of days, clicked Recover, and Time Machine sat with a box saying RECOVERING (or something of the like), which finally went away. I waited a while longer, then started looking for something I could recognize as the recovered sent mail. No sign of it.
I tried REBUILD, and nothing happened. I looked through On My Mac and also found nothing so far, although I may not have clicked on every single folder.
Does that help?