How can I fix 'connections to the server timed out' error in Sequoia 15.3.1 Mail app?

Since the latest auto-update to Sequoia 15.3.1, I can no longer access any of my mail servers to get mail from 6 different accounts. Connection Doctor shows their statuses as "offline" and there is a little triangle with an ! in it next to the names in the mailbox listings.

Says that either "Could not connect to this IMAP server. Check network connection and that you entered correct info in Account prefs. Also verify that server supports SSL. If it does not, deselect the "Use TLS/SSL" checkbox in the server settings of account prefs"; or Trying to log in to SMTP account failed. verify username and password are correct"

Note that these were all working until the update, I've touched nothing and it's now a mess times six.

Before you tell me to "just back up to last week and it should work"...or "did you try a hard reboot"...I did. (Just so we can save use both time and breath on that one :-). )

I want to know what happened and how to fix it, please. Thank you in advance.

[Re-Titled by Moderator]