This may be along the lines of what you’re suggesting, but what if you flipped this around: instead of trying to recognize AI, you recognize the student? You model each student’s quirks so you can tell if they wrote their essay, or if someone else did. Now you don’t care about AI specifically; you just care about whether they wrote what they submitted.

The main failure mode I see here is students dramatically improving and throwing the system off. If someone gets a tutor or goes to writing workshops, you don’t want to accuse them of plagiarism just because they got better. But there may be ways you could deal with that, like having the student submit new samples.