Those are examples of Jesus forgiving peoples' sins. People can't forgive other peoples' sins.
We cannot forgive sins against God only he can.
But if one trespass against you he has sinned against you.
We are asked to forgive to follow the example of Jesus.
If I waited for some in my life to repent before I would forgive I'd be drinking poison and expect a healing.
Forgiveness reflects the heart of the person. I've seen people apologize to another for a offence and still feel bitter toward that person.
Jesus said "forgive them for they no not what they do" . I believe in some situations the implications of the trespass goes farther than what is seen or heard.
Sort of like a spark near a gas can. Forgiveness can be the extinguisher .
Forgiveness spoils the plot of satan to ruin your prayer life, to harden your heart, to cause bitterness, in the hearts of those who try to walk upright.
Flesh will be flesh. Expect rumors, lies, miscommunication, backbiting, gossip, hatred, evil, contempt,
These are the works of satan to enter in the hearts of the up right to rob them of the joy and peace that God has given them. To discredit there testamony, to bring them to a place of shame and become imprisoned by there own pride or self righteousness.