Congratulate the mother on the birth of the baby. It's the right thing to do. YOU might not be excited about the new baby, but the mother certainly is excited. Why would you want to ignore something to significant? Seems petty to me......
As for the lack of announcement....perhaps it is a privacy issue for her. She might not want her business out there for the world to see. That doesn't mean that she is not excited about the new baby, though.
Take her a lovely card and a small gift for the baby. You'll feel good for doing so.