As a CS prof I have graded quite a few essays in the last year, many of them AI influenced. It's true that generic ChatGPT has a recognizable writing style, but judging human from machine can be quite hard. This is because of two reasons.
1) Sophisticated prompts on the part of cheaters
2) Off-brand AI
Just as you can recognize generic ChatGPT verbiage, smart students can as well. They tell the machine to remove the adverbs, bullet points, ornamental language, and to put things more plainly, etc. But I think I've actually had more trouble with issue (2). There was one student in particular who set off my alarms only on his 3rd exam. When I looked at his 1st and 2nd it was obvious that he had cheated on those as well. But the problem was that his AI was an idiot, and so what it said sounded very plausibly student-ish. There were awkward unworkable metaphors and circumlocutions of just the sort that bullsh*tting students use when they don't know an answer, but it was still allowing him a definite edge. Anecdotally I've heard that this might have been the Snapchat AI, but I'll never know for sure.
Incidentally one side effect of AI cheating is that when you have 30 students and you've busted 10 of them for cheating, morale declines and the social atmosphere becomes toxic. I do let students use AI quite a bit, just not on everything. About 1/3 of people try to find a way to use it anyway.