According to the RCC catechism...
1440 - Sin is before all else an offense against God, a rupture of communion with him. At the same time it damages communion with the Church. For this reason conversion entails both God's forgiveness and reconciliation with the Church, which are expressed and accomplished liturgically by the sacrament of Penance and Reconciliation.
So it's not enough that God forgives a sin. Sin is actually a rupture between the member and the Church, and forgiveness is "expressed and accomplished" by the "sacrament of Penance and Reconciliation."
Nothing about "showing repentance" directly to God. Everything about undergoing a sacrament administered by the RCC hierarchy.
I admire your patience, Dr. Eckleburg. But I do not think that arguing any Christian doctrine from the Scriptures with one who cannot even accept what the Scriptures say about their own authorship is going to go anywhere. You are arguing the material principle of Christian theology with someone who simply does not accept its formal principle ... as you manifestly do. As Jesus Himself said to the willfully blind Sadducees, He could also have said to all such who deny the plain, simple, and unambiguous sense of the Scriptures’ words, “You are mistaken, not knowing the Scriptures nor the power of God.” (Matthew 22:2)
That's actually not true. Each time I have availed myself of the Sacrament of Reconciliation, the priest directs me to express my repentance and sorrow for my sins to Christ.
I am telling you this, because it's true. I'm not interested in an interrogatory about it.
By your example (1440 of the Catechism) because it speaks in this one passage only of the sacrament of penance and reconciliation, it is tantamount to extracting one line from a car manual about adjusting the mirrors and condemning it because that line doesn't tell you about unlocking the doors. If you are truly interested in learning, then you might wander further afield than in the same exercise in Scriptural extraction that forms the basis of, for example, the Westminster Confession.