I'm honestly surprised they don't upload the entire image to apply the watermark server-side, to the point that I'd like someone else to repeat this investigation and confirm it's not happening.

Shipping the watermark generator on user's machine would make it very easy for someone motivated to find how it works and write a "watermark remover".

It is already fairly trivial to write a universal watermark remover, an LLM can do it for you.