Outgoing Mac Mail has quit working on all devices

I use Mac Mail to aggregate all of my email addresses. I have an MSN.com, several gmail addresses, iCloud, and Verizon.net (on AOL servers). I've never had any problems - not for 15 years. But suddenly three days ago I cannot send emails from Mac Mail. They go to an outbox and then the message comes back that it cannot send. I'm still able to receive and read all of my emails in Mac Mail.

This is happening on my new MacBook Pro (used for 2 months), my old MacBook Pro, and my iPhone. What could have happened that none of these devices are now sending through Mac Mail? Of course I can go to the web interfaces of my various accounts in order to send or reply, but that is an inconvenient option. I have tried the following:

--restarting my computer

--deleting the account and re-adding it

--creating and adding a new email account

--inspecting the port settings

--deleting a number of old emails

Why is it all of my devices and all of my email addresses?