There’s an issue I’ve encountered a couple of times lately, where the SMTP server for an account will report in Connection Doctor that it doesn’t need authentication (even though it does) and fail to send mail.
There appears to be no solution to this, as all the settings will be correct, the only option is to delete the account in mail.app, and recreate it from scratch. Deleting just the SMTP server profile does not appear to be sufficient to do the job.