I'll not be using it but good effort though.
The full text isn't stored on the servers, but you can always just deploy it yourself for maximum privacy:
https://dev.languagetool.org/http-server
Furthermore, there are options for docker: https://github.com/languagetool-org/languagetool#docker
For my Ubuntu machine as a client, I just use the web extension for Firefox and I also use the Visual Studio Code extension. I am most happy that my READMEs don't have such stupid errors anymore when I push them publicly where anyone can see. LOL