Comment by charlie0

> Doesn't seem like a good idea for extensions to be accessing local resources though.

To the best of my knowledge all localhost connections are exempt from CORS and that's in fact how the 1Password extension communicates with the desktop app. I'd bet Bitwarden and KeePassXC behave similarly

You can self-host Languagetool and use it as a Chrome/Firefox extension. The extension talks to a Languagetool server via HTTP, and takes its address as a configurable option. So you just run the local server, and pass localhost:8080 as the server address.