Grammarly offers autocorrect in the browser extension. Same feature is also available for Grammarly Keyboard (iOS).
What you are asking basically requires inline GUI implementation because users should be able to revert autocorrect changes. Hence you should use a web browser to take advantage of the autocorrect feature in Grammarly.
There is this community plugin LanguageTool which could implement such feature if you post a feature request there.
Related feature requests
You can edit markdown files in VS Code which can be run in browser
Obviously compatibility with browser extensions in VS Code is not guaranteed so you may need to use different more minimalistic web markdown editor with Grammarly.