I think this is overblown, the watermarking is just enforcing a particular recognizable output text style.
The existing Claudisms like "smoking gun" and "it's not x it's y" evidently haven't impacted the model's agentic capabilities much, and i doubt the new ones will either.
But it means we are optimizing for something else than the best outcome or not? It is like with mp3 vs flac: mp3 is fine and optimizes for amount of data to represent a certain waveform, but lossless is the real deal for audiophiles and the only one capturing the real thing at a certain resolution. Same might be true for complex code or the best solution to a compression algorithms. Can the question really be answered if optimizing for marking does still produce the best result? Is it not like an author wanting to say something one way, but being forced to use certain words to get there?