My other half is a non-native English speaker. She's fluent but and since ChatGPT came out she's found it very helpful having somewhere to paste a paragraph and get a better version back rather than asking me to rewrite things. That said, she'll often message me with some text and I've got a 100% hit rate for guessing if she's put it through AI first. Once you're used to how they structure sentences it's very easy to spot. I guess the hardest part is being able to prove it if you're in a position of authority like a teacher.
Are you guys using free versions of terrible tools? Asking it just to rewrite the whole thing? I use it every day for checking academic figure legends and such, and get extremely minor edits — such as a capitalization or italicization.