There are two versions of the LanguageTool: open source and cloud-based. Open source checks the individual words in the dictionary just like the system's spell checker. Maybe there is something more to it, but in my tests, it did not fix even obvious errors. It's not an alternative to Grammarly or this tool.
https://github.com/languagetool-org/languagetool
I generally run it in a Docker container on my local machine:
https://hub.docker.com/r/erikvl87/languagetool
I haven't messed with Harper closely but I am aware of its existence. It's nice to have options, though.
It would sure be nice if the Harper website made clear that one of the two competitors it compares itself to can also be run locally.