Apology is the atomic energy of empathy. Apologies make bad things start to stop happening. Apologies stop bad things from starting.
Keep in mind that while it’s true that apologies are admissions and have consequences, failure to apologize causes severe, sometimes irreparable, continuing damage and victimization. In real life, an apology is a leadership decision, rather than a purely legal decision. The sooner you make it and do it, the sooner things can start getting better.