What I've done a few times is have the AI provide feedback, and then I rewrite myself based on the feedback. So I don't use what the AI suggests directly, just the essence if I agree.
That's a good approach. My sin is that if I like the sentence, I keep and don't rewrite. Because if I see it is good, I don't feel I should. And probably I don't see that "prose" is bad each time it is indeed bad.
Maybe you should just patch a grammar problem instead of rewriting the whole sentence. (I'm not blaming you but just sharing my experience, I suspect your first language might be a Slavic one like mine.)
Well, to be completely honest with you, it is obvious in your comments here. But my point was, keeping your Slavic accent and fixing the most glaring places with the help of AI is probably better than letting AI rewrite large portions of your text into "Better English". People do hate the AI accent these days, you know.