There are two parts to this answer 1) Mailsystem configuration and 2) Mailsystem template suggestions.
1) Mailsystem configuration
This solved the issue for me and I was perhaps being silly:
Go to /admin/config/system/mailsystem and set Mime Mailer as your default config, well I want that as default.
Then below I had webform config for all webforms, but this was overkill as the settings above already made webforms use Mime Mailer, what I needed to do was add an override for this one email handler:
The specific email handler machine name was email so you can see its key is "email_email".
2) Mailsystem template suggestions
Something I learnt while investigating this is that there are template suggestions added by mimemail.module of the following pattern:
$suggestions = "mimemail_messages__" . $variables['key'];
So the above webform email, if using mimemail would use a template named