Don’t apologize to make yourself feel better. Apologize to make it right for them.

An apology aimed at your own discomfort is a request. You want the guilt to stop, so you ask for reassurance, and the other person ends up doing the work of comforting you about the thing you did to them. That is why some sorries leave everybody feeling worse. The giveaway is how much of it is about your intentions and how little about their week.

Write the sentence so it would still be worth saying if they never forgave you. Name the specific thing, skip the explanation of why you are not really like that, and say what you will do instead. Then let them respond however they respond.