Here is an update.
I believe that this is an Apple problem relating to the way the Mail app interacts with Settings. This is for two reasons:
First, because the settings that I have for the mail account in question work perfectly well to access my mail on the web.
Secondly, because they also work in Outlook, which I am now using as the Mail app no longer allows me to send mail, insisting that either my email address or password are incorrect, which they clearly are not.
This is starting to affect my mental health, causing me severe anxiety issues. I can’t believe that this is an issue unique to me!