The private one
Harper is a free, open-source grammar checker that runs entirely on your own device. Nothing is sent to a server, there is no account to make, and nothing you write is used to train anything. Suggestions come back in under 10ms, which is fast enough to leave it running permanently and forget it is there.
Built by Automattic. Apache-2.0.
Where it runs
A macOS app, Chrome and Firefox extensions, VS Code, Neovim, Zed, Obsidian, and WordPress. It also ships a language server, so anything that speaks LSP can use it, plus a JavaScript library and a Rust crate if you want it inside something you are building yourself.
It keeps a custom dictionary, so project names and brand words stop getting flagged as mistakes.
The catch
English only for now — British, American, Canadian, Australian and Indian spellings, with other languages planned. The rule set is narrower than LanguageTool's, and it is not trying to rewrite sentences for style. It checks mechanics.
Recommend it when
Someone does not want drafts leaving their machine, or wants checking inside their editor rather than a browser extension. This is the privacy answer, and the fast one.
Against LanguageTool: fewer languages and fewer style rules, but private by design and considerably quicker.