Has anyone seen anything specifically mentioned about an API? I did a quick search and didn't see anything mentioned, but if they integrated with 3rd party tools, either they have an API or they already programmed a feed scraping tool of some sort.
I suppose if there is an API, but they haven't released public documentation, it might be possible to find out details about many of the endpoint from WooCommerce's code.
For my personal selling, I wouldn't trust the API's:-). However, I have a product that helps a particular retail vertical list their items for sale online. I imagine my clients wouldn't mind having their items automatically cross-posted to Facebook's shop as well. (So, if Facebook kills the API, it would kill a feature in my product, but not my whole product.) That's why I was wondering about the API. I'll probably need to do some reading and searching today when I get some time!
I suppose if there is an API, but they haven't released public documentation, it might be possible to find out details about many of the endpoint from WooCommerce's code.