AFAICS, there is no way, short of parsing the HTML page, to determine that a user page is a global user page.
There should be a way to determine this via the API, probably as a page property or maybe in userinfo.
It should also be possible to load the global user page from the local user page, using the API. i.e. expose sufficient information for the user-agent to determine which API endpoint should be queried to get the raw wikitext of the user page (and any subpages also hosted on the global site).