I've grappled with this before, and even before people were using AI, take home exams were always open-book by default because of course people will look things up. The irony is, since AI, I've had a lot worse essay submissions-- they simply get shit wrong a lot more relying on AI (especially in my statistics class).
And my stats class only needs to do basic stuff to show work; I let them use excel/sheets to check work. They can't even type in "=correl()" properly and would rather take a photo of the data and send it to ChatGPT. AI gives them wildly wrong steps and it's so obviously wrong...