Who is the pardoning authority for Sin against the Holy Spirit?

Since you commented "Both Trinitarian and Non-Trinitarian" viewpoints are welcome, I'll try to answer based on what I believe.

God is One

I am not exactly sure what a Trinitarian and a Non-Trinitarian believes, but I believe "God is one" according to the following verse.

Hear, O Israel: The LORD our God, the LORD is one. Deutronomy 6:4.

I also believe Jesus is the Lord according to the following verses

The first man is of the earth, earthy: the second man is the Lord from heaven. 1 Cor. 15:47

and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son. Zech 12:10b

Note in the above verse, the Lord of the old testament says "They shall look upon me whom they have pierced". But God the Father was not pierced, Jesus was. The Bible can't contradict itself. The only solution is that the Son and the Father are one and the same.

The following verses says Jesus is the Holy Spirit.

The first man Adam became a living being"; the last Adam became a life-giving Spirit. 1 Cor 15:45

The following verse says the Lord is the Holy Spirit.

Now the Lord is that Spirit: and where the Spirit of the Lord is, there is liberty. 2 Cor 3:17

So, we can conclude God the Father, Jesus and the Holy Spirit are one and the same.

Only God can forgive sins

And the scribes and the Pharisees began to reason, saying, Who is this which speaketh blasphemies? Who can forgive sins, but God alone? Luke 5:21.

Unforgivable Sin

The verse you are referring to is

And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come. Matthew 12:32.

When Jesus spoke this verse, he means that the people can talk against him now, but they should turn back soon and when he sends the comforter as said in the below verse (after his death / resurrection), they can't blaspheme against Him and that will not be forgiven.

But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me John 15:26.

Sins can be only forgiven through the blood of Christ and if one doesn't accept Jesus (or the Holy Ghost), his/her sins cannot be forgiven.

So, to answer your question, for all sins, the only forgiving authority is God and none other. And it happens that God, Jesus and the Holy Spirit are one and the same.

First we need to know that this blasphemy actually was. In context the sin seems to be attributing God's miracles to Satan, rather than a direct personal affront to the Holy Spirit. NABRE for example says that Blasphemy against the Spirit is "the sin of attributing to Satan (Mt 12:24) what is the work of the Spirit of God (Mt 12:28)."

If this saying is taken literally, then the answer to the OP is "no one." There can be no forgiveness of such a sin, ever. But if the sin is merely attributing God's works to Satan, then Jesus may not have been issuing an absolute legal decree. St. Paul is only one example of a person who seems to have committed this sin and was later forgiven for it.

In the context of Jesus' other teachings about repentance and forgiveness, the saying may be seen as an exaggerated warning--like the example of his commandment to tear our your right eye if it causes you to sin (Matthew 5:29). For example:

• John 16:23 - "whatever you ask the Father in my name he will give you."

• Matthew 6:14 - If you forgive others their transgressions, your heavenly Father will forgive you.

• Matthew 7:7 - Ask and it will be given to you; seek and you will find; knock and the door will be opened to you.

• Matthew 18:18-19 I say to you, whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven. Again, I say to you, if two of you agree on earth about anything for which they are to pray, it shall be granted to them by my heavenly Father.

Thus, if the sin in question is to attribute God's work to Satan, then Jesus' saying is not a strict legal decree by a stern warning in the form of a hyperbole. God can forgive it. Jesus can forgive it. The Spirit can forgive it. Even disciples, as church authorities, can forgive it.