LanguageTool

LanguageTool is the closest thing Linux has to Grammarly, and for most people the browser add-on is the whole story. Install it in Firefox or Chrome and it checks your writing in webmail, forms, documents in Google Docs, and anywhere else you type into a page.

It also plugs into LibreOffice and Thunderbird, which matters because those are the office suite and mail program a lot of switchers land on. That covers writing offline, which the browser add-on alone would not.

Two limits to be clear about. The desktop app the company sells exists for Windows and macOS only, so the experience on Linux is the add-on rather than something watching every app on the system. And the free tier is genuinely a free tier: spelling and basic punctuation and style are covered, deeper suggestions and the picky checking are part of the paid Premium.

The engine itself is open source and can be run on your own machine, which keeps your writing off anyone else's servers. That route needs Java and some setting up, so it is worth knowing about rather than something to attempt in your first week.