If I get a response from the OpenAI API (or whatever), the fact that the text is embedded in a JSON object that is obviously an AI response, and even tells me which model was used and how many tokens it took, then I already have a machine-readable format clearly identifying the text as AI-generated. Whether the recipient chooses to keep that when they use the text is not my problem, right?
As the API provider, I would be very happy to consider myself compliant based on this. But I have a feeling it wouldn't fly in Brussels.