People do not have the authority to forgive sins against God.
Any words or deeds that break God’s laws, like murder, rape, theft, etc., - those are sins against God.
The Bible nowhere states that a person, you or I, can absolve anyone of the guilt of their sin.
The Bible does say that we are not to seek vengeance when someone wrongs us. So, for example, if someone steals our lunch, then eats it, we are not to seek revenge on them.
In terms of our “forgiving” them, let’s look at two hypothetical cases:
1) they come to us and admit they stole our lunch and ate it, they say they are truly sorry, they will give us restitution, and they say they will not steal again.
2) they giggle and deny they did it.
In the second case, they are an unrepentant sinner, and if we say we “forgive” them, they are a person who has broken the 8th commandment, so they have an issue between themselves and God, and it is not within our power to control what God does with them. While they also wronged us, we Biblically should seek restitution (not vengeance), but, if it’s not forthcoming, to be able to move on and not have it drive us “nuts”. This is easy with lunch money, but with more serious crimes it can be difficult. This is what is meant by the “crying out for God’s justice” in nations where the civil government does a very poor job of prosecuting criminals.
In the first case, they are a repentant sinner, and our forgiveness of them insofar as they wronged us would be called for, Biblically, since we are also a sinner. But we should also be seeking restitution, Biblically, from them. Of course, we should also confirm, just in case they “forgot” or are unaware (lest they neglect this), that they need to pray to God and seek forgiveness in Jesus’ name, and they need to seek after the Lord.
How many children over the years had a parent march them back to a person or business that they stole some little thing from, have them return the item and apologize - many thousands.
Not so much any more.
Even that could only be a model, an illustration, of the true attitude towards God.
Someone who wronged me years ago is not beholden to me. To force me to make them beholden to me is not of God. It is of Satan.
And allowing God to close the forgiveness loop on His own has side benefits. God has already promised that whatever we give for His sake... property, whatever... will be rewarded in multiple. So someone stole $1000 from me and went to parts unknown. I give that to the Lord. I don’t go hunting for that person to hound him. Then suddenly I find $1000 in my budget that I never dreamed could be there. God paid it back.