Setting plugin subnav to active
Based on the docs and this guide, looks like you'll want to set selectedSubnavItem in your Twig template(s) to whatever the key of your selected subnav item is (moderateentries, notificationmessages, etc).

Alternatively, you could do somthing similar to what Andrew Welch does in his SEOmatic plugin; he sets the selectedSubnavItem variable as a keyed item in a variables array and then right after that renders his plugin template (including that variables array in the render method).