If you want an API call to kick off some external processing, then insert that job into a queue table and do the same thing you always did before, consume the queue out of band and run whatever process you want.
Another one that comes up is that somehow postgrest is "insecure". Of course, if you invert the problem, you see that postgrest is actually the most secure because it uses postgres' native security system to enforce access. That access is enforced onto your API, and you know what, it's enforced on every other client to your DB as well. That's a security unification right there. That's more secure.
What PostgREST does is let you stop spending months of time shuttling little spoonfuls of data back and forth from your tables to your frontend. It's all boilerplate, install it in a day, get used to it, and move onto the all those other interesting, possibly-out-of-band, tasks that you can't get to because the API work is always such a boring lift.