when I checked to see if I could activate OnStar on my 04, best I could tell... OnStar was no longer supported for my model year any longer. There was a change in satellite frequencies or some other technology shift preventing communications. I could not activate anything other than Sirius XM.
So at this point, the OnStar mic might as well hold your sunglasses...
You might be able to wire that mic into whatver hands-free radio you are using, but might not be worth any effort on that. Even microphones have evolved to where a mic that comes with radios now for hands-free calling and voice commands is probably much better than they were 20 years ago. The mic that came with my Boss Audio head unit is really clear according to people on the other end of my calls.