This answer is based on the theology and Bible interpretations written by the Christian theologian Emanuel Swedenborg (1688-1772), which are accepted in the "New Church" or Swedenborgian denominations. Swedenborg and the various Swedenborgian denominations explicitly reject substitutionary atonement theories such as Anselm's Satisfaction theory of atonement and the Penal Substitution theory that developed within Protestantism.
Background: Isaiah 52:13-53:12 in its original context and meaning
As a background to the commentary below, it should be recognized that in its original context and meaning, Isaiah 52:13-53:12 is not necessarily about an individual at all. It is the fourth of four "Servant Songs" in Isaiah in which the "servant" is most naturally read to refer collectively to Israel, or the Jewish nation. The other three Servant Songs are found in Isaiah 42:1-9; 49:1-7; 50:4-11.
Though Israel is not explicitly identified as "the servant" in Isaiah 52:13-53:12, it is in Isaiah 49:3:
And he said to me, “You are my servant,
Israel, in whom I will be glorified.”
For other passages in the same prophet in which Israel (or Jacob) is identified as the Lord's "servant," see Isaiah 41:8; 44:1-2, 21; 45:4; 48:20.
Jewish commentaries regularly identify Israel collectively as "the suffering servant." See, for example: Isaiah 53: The Suffering Servant at aish.com.
Christian commentaries sometimes do recognize this, but they also interpret this and the other Servant Songs as prophecies of Jesus Christ. Here is an example of a Swedenborgian Christian commentary that recognizes the collective meaning of the suffering servant as referring to Israel as a nation, but still prefers to read Isaiah 53 as about an individual:
Considerable prominence is given to this subject in chapters 40-53 of this prophecy. Usually the term refers to Israel as a nation. (See 41:8-16; 42:1-7, etc.) But here in chapter 53, it points to an individual, who is undoubtedly the Lord Jesus. (The Sower by William Worcester, vol. 3, p. 207. 1941, Boston: Massachusetts New Church Union, link added)
For an online version of Worcester's commentary on Isaiah 53, see: Isaiah 53: Who Hath Believed Our Report?
Though it is certainly legitimate for Christians to interpret the Servant Songs as prophecies of Jesus Christ, this should be done with an awareness that this is a reinterpretation of prophecies that most likely were originally about the Jewish nation.
More to the point, these prophecies were not about any "substitution," still less "penal substitution," as a means of atonement—a concept that was and still is alien to Jewish theology. This becomes important as we examine the language of Isaiah 53, and specifically of the verses quoted in the question.
A more accurate translation of Isaiah 53:4-6
Christian translations of the Bible commonly bend its language toward the particular Christian theology and interpretation of the translators. This has taken place in Christian translations of Isaiah 53:4-6. Here, for example, is the King James Version (KJV) translation of these verses, which has had a heavy influence on later Christian translations.
4 Surely he hath borne our griefs, and carried our sorrows: yet we did esteem him stricken, smitten of God, and afflicted. 5 But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. 6 All we like sheep have gone astray; we have turned every one to his own way; and the Lord hath laid on him the iniquity of us all.
Providing a detailed analysis of this and similar translations would expand this answer far beyond a length acceptable on this site. So I will focus on one particular translation issue, and then provide a more literal and accurate translation of all three verses.
The first half of verse 5 is commonly translated according to the pattern of the KJV: "But he was wounded for our transgressions, he was bruised for our iniquities" (italics added).
The word here translated "for" is the Hebrew מִן, in in its prefix form of מְ. Its primary meaning (as seen here) is not "for" but "from" or "as a result of." Translating it as "for" in this context stretches and poorly represents the meaning of the word. Though most Christian translations have followed the lead of the KJV, some have more accurately represented the Hebrew, usually translating it as "because of." For example, the Lexham English Bible (LEB) translates the first part of Isaiah 53:5:
But he was pierced because of our transgressions,
crushed because of our iniquities;
Here is the LEB translation of Isaiah 53:4-6, which follows the original Hebrew much more closely than most Christian translations:
4 However, he was the one who lifted up our sicknesses,
and he carried our pain,
yet we ourselves assumed him stricken,
struck down by God and afflicted.
5 But he was pierced because of our transgressions,
crushed because of our iniquities;
the chastisement for our peace was upon him,
and by his wounds we were healed.
6 All of us have wandered about like sheep;
we each have turned to his own way;
and Yahweh let fall on him
the iniquity of us all.
Just as understanding the original context and meaning of the Servant Songs in Isaiah provides an awareness that the text as written had nothing to do with substitution, still less penal substitution, so a closer and more accurate reading of the original Hebrew shows that the language itself does not support penal substitution.
Specifically, the text does not say that the suffering servant was pierced for our transgressions and crushed for our iniquities, but because of our transgressions and because of our iniquities.
And this more accurate reading of the text forms the basis for rejecting substitutionary atonement theories as a correct or valid interpretation of Isaiah 52:13-53:12.
Isaiah 52:13-53:12 as understood in Swedenborgian theology
In Swedenborgian theology, similar to the Christus Victor theory of atonement that reigned, along with Ransom theory of atonement, as a, if not the, primary theory of atonement for the first thousand years of Christianity, Christ did not achieve atonement and redemption by substituting himself for us, but rather by achieving victory over the powers of evil for us, and thus saving us from the power of evil, the Devil, and hell. This made it possible for us to repent from our sins and begin a new life of believing in the Lord and living a good life according to his commandments.
Isaiah 52:13-53:12, according to this view of atonement, speaks of the suffering and struggle that Jesus Christ suffered both at the hands of corrupt earthly religious and political authorities and in his battle against the rampant power of the Devil, which threatened to overwhelm humanity.
Here is Swedenborg's fullest exegesis of Isaiah 53:5:
"But he was pierced due to our transgressions, bruised due to our iniquities; the chastisement of our peace was upon him, and by his wound is healing given to us" (Isaiah 53:5)
These things are said about the Lord [Jesus Christ], who is clearly the subject of this chapter. These words describe the temptations he went through in the world in order to subjugate the hells, and reduce all things there and in heaven into order. These grievous temptations are meant by his being "pierced due to our transgressions and bruised due to our iniquities," and "the chastisement of our peace being upon him." The salvation achieved in this way is the meaning of, "by his wound is healing given to us." "Peace" here means heaven and eternal life for those who are joined with him. The human race could not possibly have been saved unless the Lord had reduced everything in the hells and the heavens into order, and at the same time glorified his humanity. These things were accomplished through the temptations allowed into his human nature. (Apocalypse Explained #365:31)
What Swedenborg is saying here is that the piercing, bruising, and chastisement of the suffering servant—whom he, like other Christian theologians, interprets as prophetic of Jesus Christ as our Savior—are references to the "temptations," or spiritual trials and sufferings of Christ as he faced, battled, and overcame the full force of human evil.
In Swedenborg's theology, hell (often referred to in the plural as "the hells" collectively, meaning the collection of all the various areas and regions of hell) is the eternal abode of all humans who chose evil over good in their life on earth, and went on to live in hell rather than in heaven after death. And in Swedenborg's theology, "Satan" and "the Devil" are not understood as a fallen angel who rules hell, but rather as personifications of hell itself. Hell therefore consists of the collective evil of humanity.
So when Jesus fought against the power of the Devil and hell, he was fighting against human evil. And when he suffered inner, spiritual anguish in those temptations (as pictured in his temptation in the desert after his baptism and in his anguish in Gethsemane before his crucifixion), he was being "pierced due to our transgressions" and "bruised due to our iniquities." It was, in fact, human evil that was inflicting on him the pain and suffering that he endured in fighting against and overcoming the power of the Devil.
And because Jesus faced the full force of all human evil, Isaiah 53:6 says, "the Lord has laid on him the iniquity of us all." In other words, the Lord faced the entirety of human evil, bearing the full brunt of its crushing power in his own spirit and person, suffering everything that it could unleash upon him, and achieving the victory over it that freed us from its power.
Through that victory over the power of evil, Jesus Christ brought peace and healing to us. Without that victory, we would have been overwhelmed by the rising power of evil in human society and in the collective human heart. But by defeating that rampant power, Christ reduced the Devil, or hell, back into order and balance with heaven, restoring our spiritual freedom to choose between good and evil.
As a human example, consider a soldier going out with a defending army to repel the attack of an invader who is bent on conquering and enslaving his or her country. That soldier may be pierced, bruised, and even killed in the defense of his or her country. And the suffering and dying of that soldier and that army brings peace, safety, and salvation to the people of their country.
In the case of Jesus Christ, however, the "attacking army" was the full force of all human evil. And the "country" he was protecting was all of humanity—or at least, all who are willing to accept his saving power.
Conclusion: Isaiah 52:13-53:12 is not about substitution, but about battle and victory over evil
If we read the original Hebrew carefully and accurately, and consider its original context and meaning, it becomes clear that it has nothing to do with substitution, still less with Jesus "paying the penalty" for our sins.
Rather, it speaks of Jesus Christ suffering due to the evil and sin of humanity. It speaks of Jesus Christ facing the full force of all of human evil, going through terrible pain and agony as it attacked and sought to destroy him, even to the point of his suffering an excruciating death at the hands of evil and corrupt human beings—and yet overcoming and emerging victorious over that vast force of human evil.
This brought salvation and peace to those who are willing to accept it from him by believing in him and living according to his commandments. And we are able to do this now that Christ's hard-fought and punishing victory over the power of evil has saved us from being overwhelmed by the power of the Devil and hell, and has thereby restored spiritual freedom to us.