LanguageTool exists, although there has been some discussion about removing it. You should be fine if you self-host it. I still use it, just not for anything personal.
Harper is great but kind of basic compared to LT or Grammarly. Works well for me in Zed. [Discussion]
LTeX is pretty basic, but very simple to use and doesn’t require installing. [Discussion]
In my opinion, the best results come from LLMs. If you have the means to run a local one, I think it’s worth it. Yes, they do hallucinate and sometimes insert obvious “AI writing,” but in my experience they catch dumb mistakes and provide some nice rewrites if you ask them to. Especially useful if you have to write a lot and don’t have much time to double-check everything.