This article also answers:

I don't see the Push to Live Site option for my email notifications. Why?


Yes, there is. This option is separately available for each email notification. 

Just navigate to Settings >> Email Notifications (under Customer-facing essentials). Now click on the email notification you'd like to copy and hit the Push to LIVE Site option. Here's a screenshot. 

Note: This option will be visible only if your TEST site has a LIVE version. 

More information on this here.