Accountability with an audience is performance. Accountability alone is character.

Admitting fault in front of people carries a reward, and the reward can quietly become the reason. There is nothing wrong with a public apology, but it proves little on its own, because the same words work perfectly well as reputation repair. What you correct when nobody will ever find out has no payoff attached, which is exactly why it counts.

Find the thing you got wrong that went unnoticed. Fix it anyway, and skip telling anyone you did. The unwitnessed version is slower and less satisfying, and it is the one that changes who you are.