Yes, I know. 2022 vs. Drupal 7 and HTML mails: yikes. Sometimes you can't decide.
I need to send messages as HTML mails programmatically. I already use mime mail, previewable e-mail templates, and smtp. First of all, I found that it is necessary to configure the "Plain text body" in the templates in order to have e-mails sent out via a transactional e-mail provider. I don't understand why, because it works fine locally on mailhog without (plain text message is automatically created), but anyways. This link https://www.drupal.org/docs/7/modules/mime-mail/theming-html-mail-sent-through-mime-mail describes how to customize the e-mail template: mimemail-message.tpl.php should be copied to the used theme folder. However, the description kind of misses the point in where to exactly place it. It took me a while to find out which theme was exactly used (in my case the seven theme, which is used for the backend). The next hurdle was the mail.css: I couldn't really figure out from where mime mail would pull the CSS from, so I included all CSS needed into the e-mail template (which is necessary anyway, because e-mail programs apparently need that inline). Any change to the template file needs a cache clear to get effective.