There were no NT *priests* when Jesus gave that instruction and that idea of reconciliation has to do with individual believers and personal disputes, not a blanket delegated authority to forgive ALL sin.
The priesthood was done away with when Jesus became our great high priest.
The book of Hebrews addresses it more than clearly.
If I am in dispute with my believing brother and we discuss it and confess the sin and the other forgives, then the matter is settled, not to be brought up again. It’s a done deal and reconciliation between believers have been accomplished, which is NOT done when a person doesn’t confront the other person with whom they have the disagreement.
From what i see we are to forgive the ignorant, and while provision for redress of personal injustices is provided for, (Mt. 18:15-18) not in vengeance, but perhaps for discipline and peace in upholding holiness, yet the higher call is to allow one to due us wrong, (1Co. 6:7) if not in a continual practice.