Mail successful Mail(2) not sent?

Have you checked the Spam folder?

Yes. Not in spam or trash.
Notes/documentation for the plugin say that if there’s a problem with mail(1), then mail 2 won’t be sent. I can’t find a problem with mail(1) because those go out.

See Setting up mail

What email settings do you have in the Mail tab panel?

To protect personal data, hiding email addresses in the settings or replacing them with dummy addresses is strongly advised. Or, you can include screenshots of the admin page.