Grammarly is by and far the most popular grammar checker you can use. Not only does it look for grammatical errors, but it checks your spelling and aims to improve readability too. It can cut down on wordiness, passive voice, and repetitious use of words. It can also make suggestions to better align your writing with your audience and overall intent. Grammarly has also added AI features that can help generate text, rewrite passages, and more.
I use a grammar checker which probably corrects every single sentence I type. One should just bear in mind though that a grammar (or spell) checker needs access to every page you visit/type in order to make any suggestions or corrections.
But what I found most intriguing in this linked article, is that LanguageTool was not listed. It supports around 30 languages and installs in just about everything you can think of. Its free tier has a limit of 20,000 characters per text field, and sentence rephrasing by AI is limited to 3 per day, but it is otherwise an excellent free tool to use. It is German based, so under GDPR and funded by the EU, but their privacy policy on their site actually refers to the use of the website. Their core product though is open source, so you can host it yourself in a Docker container.