I believe that Edge is a. too new and still in development and b. Microsoft only does add-on stuff through updates or the app store.
As far as IE 11 goes there is a setting that prevents this (smart screen or something), previously you could disable that. But I think that avast have found this to be a hassle and have stopped trying to install the AOS add-on on the latest MS browsers.
I don't know this for sure as I neither use IE11 or Edge, not having win10, but there are many such topics I have seen.