Yes, exactly, that is my understanding as well. Since the watermarking is based on a symmetric key by design (as to not be easily able to test and remove the watermarks), the providers will need to offer a watermark detection API.

I see even more problems with this. To check any text for those watermarks, it needs to be sent to dozens of AI companies to check, potentially paying them all for just determining whether it matches their watermark, and more concerningly sending all that mostly human-written, often high quality text like unpublished research or books, to AI companies that almost all proved to obtain training data through all kinds of dubious ways.