Just something to note.

Websocket connections don't enforce CORS. So that's another alternative - host all of you APIs via websockets.

This feels like a bad idea, there's a reason why we have CORS.

forget @trick-or-treat, I love it.

What happens when his users expose secrets with this thing and an attacker runs up a huge api bill? Pull the plug on this OP.

FaaS - Footgun as a Service, I hope he listens to you and takes it down. The liability on his end is potentialy catastrophic.