Using firebase-backend with a hosting site

[mg98]

I am trying to use a hosting site for my firebase backend (https://firebase.google.com/docs/hosting/full-config#rewrite-functions). Not sure if this is related to #36, but I think it's not.

Say, I have a function at functions/src/string/uppercase.endoint.ts.
I can call this function at https://us-central1-myproject.cloudfunctions.net/string-api/uppercase.

Now in my firebase.json I am configuring a site in the hope to get the same result with this URL: https://myproject-api.web.app/string-api/uppercase.

"hosting": [
	{
		"target": "api",
		"rewrites": [
			{
				"source": "/string-api/**",
				"function": "string-api"
			}
		]
	}
],

The response leaves me confused. The function (string-api) is actually called, and it returns a 404:
Cannot POST /string-api/uppercase

But the path does look correct. The same request (POST /string-api/uppercase) does work on the ...cloudfunctions.net domain.

Believe me, I have tried different variations of the source and function setting. I'm actually struggling with this issue for more than two weeks. I am in contact with Firebase support but they also can't really say, because I'm using this unsupported library.

I couldn't decide whether to post it as a bug or as a feature request for an example of how to get firebase-backend to work with a hosting site. I hope of course that it is not a bug and I am just misconfiguring it.

Either way, I am really hoping for some help here. Thanks in advance.