@matmarex has proposed a plugin that allows dots in module names:
jsdoc-plugin-allow-dots-in-modules
This would fix the annoying @memberof mediawiki.module:String workaround we've been using and we'd be able to do @memberof module:mediawiki.String
This doesn't seem to impact URLs e.g. file:///Users/jdlrobson/git/core/docs/js/mediawiki.page.module_preview.html would still be the URL
This would also allow us to document modules that themselves are functions (see conversation in https://gerrit.wikimedia.org/r/c/mediawiki/core/+/995274)