A similar setup as in Firestore Emulator REST API authentication, I cannot make it work at all.
When using Postman or the browser, I always get Not Found as a response, without an error.
My URL is http://localhost:8080/v1/projects/<project-id>/databases/(default)/path/to/doc and I am certain it is correct. (GET on http://localhost:8080 returns Ok if that means anything.)
Also, the iOS app running in the simulator perfectly connects to the emulator via localhost:8080.
I doubt it is a rules issue as one would get an error json as detailed in the question linked above.
What does Not Found mean at all?