To be more specific, we would like to make an add-on that will search also through our website (where we store the bookmarks of the user).
Right now we achieved it by creating an add-on and a search field comes out when the user presses on it.
However, ideally we would like that results will come directly in the address bar instead, since it's the most natural way for the user.

If that's possible, can you provide me with an add-on that does that in some way?

Thanks!