This seems like it should be straightforward, but I haven't had success theming the default registration emails on my site. I am able to see the themed email (just using swiftmailer.html.twig in my theme) when I send a test email via the Swift Mailer UI, but using Swift Mailer for my formatter and sender in the default mail system config in the Mail System UI and using my theme to render the emails, I'm still not getting the themed registration emails as I would expect. I must be missing something simple, but I've tried all sorts of combinations without luck.
The trick was to make sure the 'Respect provided e-mail format' option is unchecked in the message settings. Then I added a plugin to force HTML output for these email, as per this suggestion and used that for my Formatter and Sender in the mail system settings.