Hi there Samantha!
My name is John and I'm a Guru here at Shopify!
Thanks for reaching out and posting here about your notification requirements. :)
There is at least one app I managed to find that will be able to send out whatever notification you need at whatever point you wish to send it!
Check out Notifications by eShopAdmin and see if this would work out for you.
You can always contact app developers via the email address or contact form listed on every app store page. :)
Best of luck with everything here!
I made a quick workflow for you and added it to the library. https://www.apps.bonify.io/arigato-automation-shopify/workflows/email-paid-certain-payment-type