[Vuejs]-Use Vue router to set variables instead of component visibility?

My question was based on bad understanding of what VueRouter does. There is no need to add an extra navigator component like I suggested.

To achieve the goal in the question, add a router view and use the router to control its content and props. After all, we need something in the template for the router to control. If needed, the content can be a single component that is never hidden. To achieve that all paths in the router refer to that router view (or at least: all router paths for that router view).