I am familiar to quite a few tries of using Discourse as only an API and rewriting the whole front-end and it always end up badly, as people subestimate the sheer size of our front-end app. Also there is no versioned API, so while you can target our latest stable version and build your app in a few months, you will have go back every six months and fix all the compatibilities with the newly launched version.
The most common API endpoints are documented at https://docs.discourse.org/.