Sketch (Cloud) does indeed have a GraphQL API (that both the web app and Sketch.app use behind the scene) but it's not documented so you're on your own if you want to use it.
That said, I've prepared a little guide on working with this private API and even included a section on getting a list of comments for a particular artboard/page – which seems to be what you're looking for:
https://forum.sketch.com/t/python-support-and-graphql-api/1041/4#h-26-listing-all-annotations-and-their-comments-for-a-given-artboard-or-page-12
Enjoy!