Static serving usually means you don't have anything running on the server but an actual web server, and you upload the static files to its webroot. So it's not technically possible to have any fancy editor in your browser. You have all the brains in some tool you run on your machine that processes your markup files and spits out html files.
Sure, you could throw PHP or whatnot on your server, have a nice editor and whenever you edit or add content it statically generates all the html files, which would probably technically still be called a static site generator but then I don't see why you'd want to do that instead of just going all the way and use normal blogging software and putting a cache in front.
There’s a whole category of headless content management systems, either API or git based, to give a friendly editorial experience (also for non technical editors) while maintaining the advantages of static sites.
