I'm an expert in english grammar (to be more precise, the grammars of englishes) and I just wanna say that, whether you are a native english speaker or not, AI grammar correction would be bad even if it weren't so fucking bad. There is no one way that we speak or write, and the ways that we speak and write change all the time. All a grammar check can do, even in an ideal world where the tool actually works as intended, is "correct" you to what is considered the most "appropriate" form of english, which is white mainstream english (see April Baker-Bell's work, she coined this term and it's very useful and she's amazing). Grammar check is racist, classist, sexist, US or UK-centric, and it also corrects towards the most common kinds of expressions we use - ie, corrects away from playful, creative, fresh, and experimental uses of language.
(note that lots of the diversity of english comes from its role, past and present, as an imperial and colonial language. That colonial project continues VIA THINGS LIKE MODERN GRAMMAR CHECKERS. The first english grammar for schoolchildren was developed for use in India, not in England. The concept of teaching english grammar is coterminous with the rise of the british empire and is part of the project of british empire.
Moreover, oppressed populations and non-native speakers have added diversity of expression and new dialects to english as a result of horrific colonial violence. pretty shitty to force people to speak a language and then tell them their way of doing it is wrong.)
We need to work to accept all englishes and all usages, and to reduce the shame people feel around grammar (which is also race/class/gender/sexuality/ethnicity/geographic region/etc. based! that shame is just oppression). Rather than trying to get everyone to write the same way, I suggest participating in the joy of grammatical diversity. All language has rules (all versions of english have rules), but the rules are descriptive (here's how we typically generate a sentence in my dialect) not prescriptive (here's how you ought to generate a sentence in english). There's no such thing as "proper" or "correct" grammar. There are just accepted conventions in different contexts.
If you wanna learn about those conventions, fabulous: that's called studying grammar. That knowledge will make you a better writer, because you'll understand the wide world of options that grammar gives you in writing, and you'll be able to express yourself with greater precision and confidence. But you don't gotta write any particular way.
genAI fucking blows for many, many reasons, including that it doesn't fucking do the things people think it can do with language, but one specific way in which it blows is that it moves us away from the delightful diversity of language and towards homogenized boring oppressor-speak.
If people can understand you, your grammar is fine. If they can't, they should ask you what you mean (in a non-asshole way). If you're writing for publication, you gotta learn the conventions for that kind of publication (and sometimes fight them). That's it.
Whatever your grammar pet peeve is . . . work on letting it go. It doesn't matter.
If you're new to the idea of english grammatical diversity, the Yale Grammatical Diversity Project is a great place to start - and it's really fun to find out that you say something in your english that other people don't, or vice versa!