I cannot think of a situation where an API only handles CRUD data and lacks any behaviour.
But, If your API really only is pushing data around, ' such tooling is usefull and probably saves a lot of time.
You put an item in table queue using SELECT FOR UPDATE ... SKIP LOCKED and some out of band consumer sends your email.
PostgREST isn't about doing everything in the database it's about doing all the same patterns you already do but with less boilerplate.
I'd add that you also have hard to spec couplings and difficult to manage microservices setup.
Tools like MQTT or paradigms like eventsourcing might help. But those all presume your database is a datastore. And not the heart of your businesslogic.