The person who paid for your oversight deserves a clear account of how it will be addressed.

Apology and repair are different things, and only one of them costs you anything. When your mistake lands on someone else, they are usually left holding the practical consequences while you are left holding the feeling, and a sincere sorry does nothing about their half. What they need is specific: what happened, what you are doing about it, and by when.

If someone is currently absorbing the cost of something you got wrong, go back with a plan rather than another apology. Name the fix and the date. Then tell them when it is done, without waiting to be asked.