Asking forgiveness is acknowledging the value of the person you hurt. It's why it bothers us when someone else hurts us and doesn't apologize. It's not the hurt itself but the demeaning that follows when an apology is held back.

Giving forgiveness is a good way of releasing ourselves from taking responsibility for others. It says that I don't need to be the person that teaches you a lesson, you will learn that in other ways and circumstances, but meanwhile I am getting on with my life.

You're right that hypocrisy, of which virtue signalling is part, is exposed as sinful behavior counter to the life in the Spirit. But the same Jesus who did that also taught us to forgive and to seek forgiveness. God alone forgives sin but we are to forgive trespasses (stepping on each other) and debt (where we withheld something like love or honor because we were mean spirited)