YOU ASK FORGIVENESS, then go and sin no more (try not to).
The woman in this story did NOT ‘ask for forgiveness’.
She didn’t need to. God WAS STANDING RIGHT IN FRONT OF HER IN PERSON and I suspect he sensed this....
https://www.crosswalk.com/faith/bible-study/how-could-jesus-offer-forgiveness-to-unrepentant-people.html#:~:text=Faith%20brings%20us%20near%20to%20Christ%20and%20he,sins%20of%20the%20people%20who%20are%20standing%20nearby.
A good place to start is by looking at other examples in the New Testament of Jesus forgiving people. For brevity, let’s consider other examples from the Gospel of Luke.
And when he saw their faith, he said, “Man, your sins are forgiven you” (Luke 5:20).
“I tell you, her sins, which are many, are forgiven—for she loved much. But he who is forgiven little, loves little.” And he said to her, “Your sins are forgiven” (Luke 7:47-48).
In both situations, notice that Jesus sees evidence of a person’s faith in him and then he forgives them.
What you typed here is true, but what you typed before was: “...ask for forgiveness.’
With your ‘explanation’ and my showing the actual Scripture; some lurker; who hasn’t had as much experience as you or I; would come away with a wrong understanding.