All grammar checkers are "AI"
They were "AI" long before the creation of ChatGPT or the Stable Diffusion, or whatever the other service calls themselves "AI".
The word "AI" turned into a buzzword these days, it doesn't mean anything. It used to mean something, originally, but since it was used constantly and out of context, especially by the largely ignorant marketing departments, any meaning the word originally had was lost. Now it is just "electronic stuff". My coffeemaker is "AI". It doesn't have any functions, other than turning on, heat water, and how much, but it is "AI" because there is a printed circuit inside.
If you want anything that isn't called "AI" these days, find yourself a proof-reader or editor, i.e. an extra pair of eyes (preferably someone whose first language is English if your isn't) and have them check everything ...
And if not?
Try Pro Writing Aid. It's called AI because well .... it's like my coffeemaker ...
Unlike Grammarly, however, the Pro Writing Aid creators at least assumed that someone is going to use it for creative writing and doesn't too overtly turn everything into the corporate speech.