Sure, a human author would almost never do that, but they could. I could imagine a Markdown syntax that did that – it could be done similar to how `code` is marked up in most blogs.
I wouldn't call this a watermark, but more a sign of likely copy&paste, if students' word processors weren't currently doing that.
A "watermark" that invisibly identifies the text origin using Unicode tricks sounds possible.
And maybe you could do some things with statistical patterns.
Or you could, as some have done in the past, is to stego the identifying information in a way that's hard to spot but can't be denied later (e.g., the first letter of each word clearly spells out "john smith is a cheater who copied this from chatgpt").
selcuka•49m ago