Unfortunately, the browser extension is proprietary. They used to have an open source one but they stopped maintaining it.

Proprietary was a dealbreaker for me. There is no way to verify that it isn’t selling everything I type even if I do have it configured to point at a local server.

I’m also concerned that the extension may eventually no longer work against local servers as well.

github.com/languagetool-org/…/247

As an alternative, there is harper by wordpress: github.com/Automattic/harper

It is webassembly and runs entirely in your browser.

EDIT:

I will add that the rest of the languagetool ecosystem continues to work fine. Libreoffice now has a built in client, which you can point at your own hosted server. VSCode [1] also has their own languagetool extension. I use those and those work great. But in the browser I use harper nothing. I should probably install harper.

[1] Well, technically I use [code-oss]wiki.archlinux.org/title/Visual_Studio_Code), which gets the extension from open-vsx.org