Newborns and Cats

Anyone have any stories or experience introducing your pets to your baby? I have 2 cats and am having the worst anxiety about how they’ll react to my baby when we bring him home. My younger cat has separation anxiety and is always near me no matter what (he’s even on anxiety meds) I know all animals are different but I’m hoping for a smooth transition.. I’ve had a couple people make the “cats smother babies in their sleep” comment to me and I can’t put my mind at ease about it😕