[all verses RSV]
Anti-Catholic Protestant apologist Jason Engwer wrote:
I don’t know what details you have in mind, but you’ve mentioned concepts such as confessing to a church leader and doing so in private, which you consider a development that’s “to be expected”. If what you have in mind is something like the modern Roman Catholic system of confession, then there is no justification for it in scripture. (9-11-06)
Confessing Sins to Human Beings
Leviticus 5:5 When a man is guilty in any of these, he shall confess the sin he has committed, [in conjunction with an offering of a sacrifice to a priest for the sake of atonement]
Numbers 5:6-7 . . . When a man or woman commits any of the sins that men commit by breaking faith with the LORD, and that person is guilty,  he shall confess his sin which he has committed; . . . [in conjunction with an offering of a sacrifice to a priest for the sake of atonement]
Psalm 38:18 I confess my iniquity, I am sorry for my sin. [possible; could mean the same procedure as in Lev 5:5 and Num 5:6-7]
Proverbs 28:13 He who conceals his transgressions will not prosper, but he who confesses and forsakes them will obtain mercy. [possible; could mean the same procedure as in Lev 5:5 and Num 5:6-7]
Mark 1:4-5 John the baptizer appeared in the wilderness, . . .  . . . and they were baptized by him in the river Jordan, confessing their sins. (cf. Mt 3:6)
Acts 19:18 Many also of those who were now believers came, confessing and divulging their practices
James 5:14, 16 Is any among you sick? Let him call for the elders of the church, and let them pray over him, . . .  Therefore confess your sins to one another, and pray for one another, that you may be healed. The prayer of a righteous man has great power in its effects. (cf. 1 Jn 1:9) [arguably — in context — implies confession to the elders in particular, since their prayers have more power]
Human Beings Extending God’s Forgiveness (Absolution) as His Representatives
Leviticus 4:35 . . . and the priest shall burn it on the altar, upon the offerings by fire to the LORD; and the priest shall make atonement for him for the sin which he has committed, and he shall be forgiven. (cf. 4:20, 26, 31)
Leviticus 5:5-6 When a man is guilty in any of these, he shall confess the sin he has committed,  and he shall bring his guilt offering to the LORD for the sin which he has committed, a female from the flock, a lamb or a goat, for a sin offering; and the priest shall make atonement for him for his sin. (cf. 5:10, 13, 16, 18; 6:7)
Leviticus 19:21-22 but he shall bring a guilt offering for himself to the LORD, to the door of the tent of meeting, a ram for a guilt offering.  And the priest shall make atonement for him with the ram of the guilt offering before the LORD for his sin which he has committed; and the sin which he has committed shall be forgiven him.
Numbers 14:19-20 [Moses] Pardon the iniquity of this people, I pray thee, according to the greatness of thy steadfast love, and according as thou hast forgiven this people, from Egypt even until now.”  Then the LORD said, “I have pardoned, according to your word; (cf. Num 15:25, 28)
2 Samuel 7:4-5, 14-15 . . . the word of the LORD came to Nathan,  “Go and tell my servant David, `Thus says the LORD: . . .  . . . When he commits iniquity, . . .  . . . I will not take my steadfast love from him, . . .
2 Samuel 12:13 David said to Nathan, “I have sinned against the LORD.” And Nathan said to David, “The LORD also has put away your sin; you shall not die.”
Matthew 18:18 . . . whatever you loose on earth shall be loosed in heaven. (cf. Mt 16:19)
Mark 1:4 John the baptizer appeared in the wilderness, preaching a baptism of repentance for the forgiveness of sins.
John 20:23 If you forgive the sins of any, they are forgiven; . . .
2 Corinthians 2:7-10 so you should rather turn to forgive and comfort him, or he may be overwhelmed by excessive sorrow.  So I beg you to reaffirm your love for him.  For this is why I wrote, that I might test you and know whether you are obedient in everything.  Any one whom you forgive, I also forgive. What I have forgiven, if I have forgiven anything, has been for your sake in the presence of Christ,
James 5:14-15 Is any among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord;  and the prayer of faith will save the sick man, and the Lord will raise him up; and if he has committed sins, he will be forgiven.
Human Beings Issuing Penance or Announcing God’s Impending Judgment for Sin
Numbers 5:5-7 And the LORD said to Moses,  “Say to the people of Israel, When a man or woman commits any of the sins that men commit by breaking faith with the LORD, and that person is guilty,  . . . he shall make full restitution for his wrong, . . .
2 Samuel 7:4-5, 14 . . . the word of the LORD came to [prophet] Nathan,  “Go and tell my servant David, `Thus says the LORD: . . .  . . . When he commits iniquity, I will chasten him with the rod of men, with the stripes of the sons of men; . . .
2 Samuel 12:7-12 [Prophet] Nathan said to David, “You are the man. Thus says the LORD, the God of Israel, `I anointed you king over Israel, and I delivered you out of the hand of Saul;  and I gave you your master’s house, and your master’s wives into your bosom, and gave you the house of Israel and of Judah; and if this were too little, I would add to you as much more.  Why have you despised the word of the LORD, to do what is evil in his sight? You have smitten Uri’ah the Hittite with the sword, and have taken his wife to be your wife, and have slain him with the sword of the Ammonites.  Now therefore the sword shall never depart from your house, because you have despised me, and have taken the wife of Uri’ah the Hittite to be your wife.’  Thus says the LORD, `Behold, I will raise up evil against you out of your own house; and I will take your wives before your eyes, and give them to your neighbor, and he shall lie with your wives in the sight of this sun.  For you did it secretly; but I will do this thing before all Israel, and before the sun.'”
Matthew 18:18 Truly, I say to you, whatever you bind on earth shall be bound in heaven, . . . (cf. Mt 16:19)
John 20:23 . . . if you retain the sins of any, they are retained. [refusal of absolution, for various reasons]
1 Corinthians 5:1-5 It is actually reported that there is immorality among you, and of a kind that is not found even among pagans; for a man is living with his father’s wife.  And you are arrogant! Ought you not rather to mourn? Let him who has done this be removed from among you.  For though absent in body I am present in spirit, and as if present, I have already pronounced judgment  in the name of the Lord Jesus on the man who has done such a thing. When you are assembled, and my spirit is present, with the power of our Lord Jesus,  you are to deliver this man to Satan for the destruction of the flesh, that his spirit may be saved in the day of the Lord Jesus.
2 Corinthians 2:6 For such a one this punishment by the majority is enough;
1 Timothy 1:19-20 holding faith and a good conscience. By rejecting conscience, certain persons have made shipwreck of their faith,  among them Hymenae’us and Alexander, whom I have delivered to Satan that they may learn not to blaspheme.
Angels Extending God’s Forgiveness (Absolution) as His Representatives
Exodus 23:20-21 Behold, I send an angel before you, to guard you on the way and to bring you to the place which I have prepared.  Give heed to him and hearken to his voice, do not rebel against him, for he will not pardon your transgression; for my name is in him.
Isaiah 6:5-7 And I said: “Woe is me! For I am lost; for I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the LORD of hosts!”  Then flew one of the seraphim to me, having in his hand a burning coal which he had taken with tongs from the altar.  And he touched my mouth, and said: “Behold, this has touched your lips; your guilt is taken away, and your sin forgiven.”
Photo credit: Repentance of St Peter (1635), by Guido Reni (1575-1642) [Wikimedia Commons / Creative Commons Attribution-Share Alike 4.0 International license]
Summary: I compile biblical data indicating a sanction of confession to men for the sake of receiving forgiveness from God; also proof that penance or “binding” is also biblical.