A public apology should not force the recipient to provide immediate public forgiveness.

An apology delivered in front of an audience changes what the other person is being asked to do. They are no longer deciding whether they accept it; they are performing a response while people watch, and any answer other than gracious acceptance will look ungenerous.

Apologize where the harm happened and to the person who was harmed, without an audience unless they want one. Say what you did, say you were wrong, and then leave room rather than waiting for a reply. If a public correction is genuinely needed, make it about the record and ask nothing of them in return.