About the saying
A commentary I consulted mentioned how St. Augustine confessed that interpreting the saying of how blasphemy against the Spirit will not be forgiven "may be the most difficult and most important question in the Bible.⁸⁷".
The commentary then prefaced the history of interpretation of this passage by noting:
There are questions on two levels. First, the exegetical question is: Of what does the blasphemy against the Spirit consist? The texts do not elaborate on it but presuppose that it is understood. The question becomes especially difficult when it is contrasted with speech against the Son of Man that can be forgiven. Second, the theological question is: Is there a limit to grace? Does this sentence not contradict the boundless love of God—thus the center of the proclamation of Jesus—and therefore also the conviction of the boundless power of the Holy Spirit?
In my answer I am going to simply follow the interpretation given by gotquestions.com article and clarify the points you raised in your question.
About the double quotes
The sentence causing your confusion is in this paragraph:
The unpardonable sin today is the state of continued unbelief. The Spirit currently convicts the unsaved world of sin, righteousness, and judgment (John 16:8). To resist that conviction and willfully remain unrepentant is to “blaspheme” the Spirit. There is no pardon, either in this age or in the age to come, for a person who rejects the Spirit’s promptings to trust in Jesus Christ and then dies in unbelief. The love of God is evident: “For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life” (John 3:16). And the choice is clear: “Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on him” (John 3:36).
When I read the whole article, the author put double quotes around "blaspheme" to signal unusual usage, a convention in English language. Why? Recall that earlier the gotquestions.org author already established that because Jesus is no longer on earth we cannot sin that very specific way anymore, the way the Pharisees did. If the author didn't put the double quotes he would have contradicted himself.
About your concluding scenario
I ask because I am wondering whether a person can be considered to speak against the Holy Spirit if they witness a miraculous healing performed with no selfish intention (such as to gain money or fame) and know that it is done without selfish intent, yet they claim that the miracle is the work of Satan.
The article author was emphatic in asserting:
Blasphemy against the Holy Spirit has to do with accusing Jesus Christ of being demon-possessed instead of Spirit-filled. This particular type of blasphemy cannot be duplicated today.
According to the article what is no longer possible is witnessing Jesus Christ's miracle in person (with our own eyes) and "then attribute that power to Satan instead of the Spirit." We cannot do this anymore because Jesus Christ is not on earth anymore. But your scenario is not the same since that person is NOT Jesus Christ, and thus maybe someone posing as a false prophet, or even the Antichrist (see 2 Thess 2:9-12). Therefore, denying that work is not the same as blaspheming the Holy Spirit.
What does this passage mean for us today?
So if we cannot blaspheme against the Holy Spirit in the very specific way the Pharisees did, what is the lesson for us today? The author then draws some common element that may still be possible today, which is continually rejecting any grace and any prompting of the Holy Spirit who tries to bring us into accepting Jesus as our savior, which he phrased as the "state of continued unbelief". God does not force us against our will. It is possible that we can eventually win this battle with God, which results in us placing ourselves in hell. C.S. Lewis is famous for his quote "The gates of hell are locked from the inside" (from The Great Divorce).
But as this article suggests, different denominations provide different answers about this possibility. My personal opinion is: why risk it? The offer of salvation is clear, let's take it before we die and really learn how to follow Jesus with our whole heart while we are still living.
I thought the one which not possible anymore is to blaspheme (speak/say a word) against Son of Man (Jesus in this case). Except I was mistaken that "Son of Man" actually is human in general not Jesus in particular.
Jesus's applying the title "Son of Man" is claiming more than being a 100% human being. Jesus was referring to Daniel 7, a title that only Jesus holds, not any of us (see John Piper's explanation). Jesus seems to be saying that speaking against him can be forgiven, which is different than blaspheming against the Holy Spirit.
You wrote : The unpardonable sin today is the state of continued unbelief ... is this specifically for the non Christian ?
Yes. It is for people who die as non Christians (according to non-universalist interpretation). But remember, this can also be for ex Christians too: people who used to believe in Jesus, but for some reason reject the faith for various reasons such as joining another religion, rejecting God because of death of loved ones, etc. But if these ex Christians go back to being Christians again before they die, God will pardon them.
In other words, it's not possible to happen that a Christian sin again, (hence no need to repent)
That is a wrong inference. Excepting Jesus, even a saint sins from time to time, and repentance is needed every single time. We are all struggling to be perfect and God expects us to repent everytime we sin and God promises forgiveness. That is why we are commanded to forgive our brothers 70 x 7 times because we need to have a character like God who is ready to forgive us as long as we repent.
Was there no sin which wouldn't be forgiven?
According to gotquestions.org article interpretation, the answer is all sins can be forgiven if we repent. Repentance is the key, the human initiative, the one we can do with the assistance of the Holy Spirit.