A real apology names what you did. A fake one just mentions that something happened.

The difference between the two is whether a specific action appears. When you say what you actually did, the other person knows you understood it, and that understanding is most of what they wanted. A vague regret leaves them wondering whether you even know which part hurt, so they have to explain it all over again.

Before your next apology, write the one sentence that names the thing: what you did and what it cost them. Say that sentence first, with nothing attached. Anything else you want to add can come afterwards, if they still want it.