How to pass contextual id value from one view page to another through Drupal menuing system
The "connected" exposed sorting criteria is implemented in the Facets module and Search API. 
Here's a tutorial that can help get you started: Creating a Faceted Search View in Drupal 8 using the Search API Modules



Before you start testing new modules maybe the "ordinary" Exposed Sort criteria in Views can help. Create only one Page display, but add all 3 Sort criteria you want and Expose them. You can use the Expose form in Block to show those options in some region of your theme instead of above the results. 

The Better exposed filters module allows you change the widgets from drop-downs to Radio buttons or links. You can also rewrite the filter options to make them more relevant for your cases, and combine the "sort order" with "sort by". 

Having an exposed form block can serve like Menu items, showing the user what has been selected, which is what the active menu trail does. 



To clean up the URLs there is the Query Parameters To URL module but it's still being ported to Drupal 8. (Help advance it if you can.) Without it I guess you can set up some path redirects manually, although it might be tedious if you have a lot of combinations to cover. You can do that in .htaccess or with the Redirect module. 



Yet another approach I can think of is the Views Global Filter module. You might use the "topic" globally, then sort links might work with menu trails (I haven't tried it).