iCloud SMTP Not Working in Apple Mail in macOS Big Sur

I have an issue with sending mail from my iCloud account. I am using the classic mac.com address and have been doing so for years. Back a couple of months ago, I had to send my MacBook Pro off for a battery and keyboard replacement, so I signed out of iCloud to send it in for service. While the computer was gone, I used a loaner MacBook Pro on which I signed into my iCloud account to use my mail on the new computer.

When my MacBook Pro returned, I signed out of iCloud on the loaner MacBook Pro and re-installed macOS on it. I then signed in to my account on my MacBook Pro and the problem began in Apple Mail.

I can receive e-mail to my iCloud account just fine, but when I try to send e-mail from that address, Apple Mail tries to send the mail, but errors out after 10 minutes or so, saying that smtp.mail.me.com is not available and asks me to choose a different e-mail server. I have tried deleting and re-adding the SMTP server for iCloud to no avail. In Connection Doctor, iCloud shows it connects via IMAP, but the SMTP server just shows the spinning cursor and never connects.

I have been trying to get help from Apple on this for the past 6 weeks. The advisors keep passing the issue up to engineering and they have yet to solve the issue. I have reinstalled macOS, reinstalled my iCloud account, turned the account on and off, trying to force a sync, but nothing has worked. The problem occurs on any network I am on.,

I might add that I can send mail from iCloud webmail and on my iPhone and iPad.

Does anyone have any ideas of what I could try to get this account to start sending mail from Apple Mail on my MacBook Pro?