People give second chances way more often to the person who told the truth the first time.

People deciding whether to give you another go are guessing about the future, and what they guess with is how you handled the last problem. Someone who came forward is easy to work with again. Someone who had to be caught leaves a question mark that never fully clears. The mistake matters less than what you did in the hour after it.

Bank some of this now, on something minor. Report the small error before anyone asks, and do it where it will be remembered: a manager, a coach, a teacher. You are not only fixing the thing, you are building the file somebody reads later.