I have experimented quite a bit with this, thought it must be my error.
But as I tried the simple project from the scratch I am more and more inclined to think that there is some bug in Xamarin.Mac. Simply the app that is not sandboxed works, and as soon as you make two steps - sandbox the app and sign it and its extension with the proper provisional profiles, the share extension doesn't work (doesn't appear among extensions at all).
Maybe there are some more steps that I should take to make this work or it is a bug?