What is the status of the intended GraphQL API for v8.1?

It’s not a folder, it’s a Symfony route ( a mapping from a URL path to a controller). It’s ready to be used (the entire SuiteCRM 8 UI runs on top of it), but Documentation is still lacking.

This post might be able to get you started, I posted a sample custom API entrypoint:

Once you can get the basics going, and understand the way URLs map to PHP classes, you should be able to find plenty of examples in the existing v8 code.