Yeah, I’m pretty sure that those paths work in backend. For example, when I visit app.example.com/dashboard/ (the subdomain with no rewrite rule) I can view the dashboard page just fine.
However, if I visit the same page via dashboard.example.com the view is completely blank. Although, in this case when I view the page source, the page has its HTML loaded and it looks like this:
However, if I change the router base property as you suggested (for example with '/dashboard` value), it simply appends the that base to JS resource uri, like so:
