Without using a checker I doubt very much that the writing is AI generated, it certainly doesn't look like a typical chatbot AI diarrhea. However, I run it through writefull and write AI and in both cases it tells me that the content is human. With sapling AI, copyleaks and hivemoderation it tells me that it is AI. According to your criteria it would be AI generated but it seems that AIs are being perfected in such a way that it is not easy for the human eye to detect them at first glance.
There is nothing wrong in my opinion with using an AI to check your spelling and grammar and the content should not appear as AI generated in the checkers for minor grammar and spelling changes.