How can I effectively translate customer notifications?

If I understand the problem correctly you’ve edited your English notifications and you want the Spanish ones to follow through but at the moment they are different.

Since Spanish is a very popular language Shopify has these notifications translated by defualt. If you want them to inherit from your English translations you’ll need to export a CSV from admin > languages > export. Go to the notifications section, delete all the default Spanish ones. Import it back to your admin. Then translate the English notifications with Translate & Adapt.

That will help you get Spanish translations of your English notifications.