this would be a very heavy watermark application.
there are many simpler methods, for example you can have a tiny windowed transformer operating on the output text and all you do is alter certain words (that don't change meanings) to maximize its surprise. the tiny language model will have a special training regime to build up a somewhat unique view of the language.
we are talking about a 0.5 bit watermark here (existence). I would have zero confidence in being able to reliably remove such a watermark from pretty much any medium.