I don’t believe our javascript plugin API is set up to make it easy to add a secondary dropdown menu at this point. The toolbar customizations I can think of have all just added options to the existing drop down.
To get something to render you would need to change your group to "extras". The groups are hard-coded and relate to the various sections of composer buttons.
The other thing to watch out for is that the icon you choose needs to be added via your theme component or the svg icon subset site setting.
Beyond that, I’m afraid you’re treading into fairly uncharted territory.