I work with RapidWeaver — Mac OS X CMS application — and it uses no server environment. It has an editor and a preview mode. The preview mode is a Web
localStorage is a html5 mechanism to give scripts a bit more space than cookies. Safari supports it: https://developer.apple.com/library/archive/documentation/iPhone/Conceptual/SafariJSDatabaseGuide/Name-ValueStorage/Name-ValueStorage.html
I don't know offhand what, if any, path restrictions it should have for file:/// based apps.
Edit: looking into the path restrictions further, I see that what you got should work with Safari, FF recently fixed a bug that would keep it from working there: https://bugzilla.mozilla.org/show%5Fbug.cgi?id=507361