If you only apologize after getting caught, you’re mostly sorry about getting caught.

Getting caught changes the arithmetic, not the conscience. If the sorry arrives only once there is no other option, what you are hearing is a response to exposure, and the person on the other end can usually tell the difference. It also explains why those apologies feel hollow even when the words are correct. Nothing in them was chosen; the situation chose it.

Notice whether you have been sitting on something nobody has found out about. Go first if you have, because the same sentence is worth far more unprompted. And when somebody apologises to you after being caught, you can accept it and still wait to see what changes.