Webform supports Symfony Mailer, and you can configure a separate mailer policy per webform handler. This can be useful if you want different theme, format or even a different sender for each of your mail handlers.
The trick is in the Symfony Mailer sub-type naming convention:
[webform-machine-name]_[webform-handler-machine-name]
For example, if you had a webform with the machine name "contact" and the standard handler "email", the sub-type becomes "contact_email".
Symfony mailer does not yet support separate email builders per webform (see issue #3260134) but setting up a separate policy may provide enough for your customization without needing custom code.