Google is said to be adding machine learning powered grammar checking to Google Docs but as far as I can tell it's not there yet.
There are various other solutions around, many we cloud back ends, but happily I can recommend the open source LanguageTool when used as an extension to LibreOffice. Note that you need to install the official Oracle version of Java for this to work. (I think I also needed the JDK but I'm not totally sure).
The grammar suggestions are very useful and while there are a few false positives, it's very valuable. As well as basic grammar and spelling errors, it has high level recommendations including things like collections of sentences that begin with the same word and ideas for simplifying text.
Microsoft Word, particularly when working with a large document (this one is over 100,000 words) and with the EndNote app feels quite flakey. Several times we've seen weird errors such as being unable to save a document due to file permissions - restarting word fixed this. EndNote hangs sometimes and it, in turn, locks up Word.
LibreOffice on macOS feels solid although the user interface is not native and no where near as nice to use as Apple's Pages. I also tried it in Visual Studio Code which worked but tried to do the whole document in one go and wasn't practical.
Academic documents have their quirks and LanguageTool doesn't seem to handle references very well but over all it's been a great experience, and we've found many embarrassing typos and grammar errors that would have been submitted and printed without it. My thanks to the great people who've given us LanguageTool.
Update: Google Docs now has grammar checking
Logged in this morning and Google Docs is now offering me grammar checking and it seems very good.
I wouldn't like to be in the commercial grammar checking business.