Third Addons plugin which add emails (exemple Gift Cards) pass through the New Order template.
In WooCommerce Email settings those mail are different (separate) from the New Order, is it possible to “deviate” those emails from New Order ? If not that’s put a big limitation of the use of Email Designer for WooCommerce and really dangerous if a client ask later a addon who send email because it can destroy your previous work (if you need to disable Email Designer)