Does AI watermarking present a new attack vector?

One thing I have not been able to determine from Claude's documentation on watermarking[0] is what kind of metadata they store in association with a given watermark. Ostensibly they could make the fingerprints as unique as they want, possibly down to the exact time, user and session.

If so, this seems like hidden risk that AI users are probably not considering. Any code you write now carries information that you might not want revealed. If a bad actor gets the keys then they may be able to de-anonymous open source contributors who want to stay hidden. Or perhaps enough fingerprints across a sample could reveal internal organization details a company would rather not disclose.

Someone with more imagination can probably come up with better examples, it just seems like an attack vector that I haven't seen much consideration for.

[0] https://support.claude.com/en/articles/16266773-how-claude-marks-ai-generated-content