Are there Christian Denominations or Movements who believe that Jesus didn't actually pay our sin debt?

It is possible that the movement called “The New Church” (which came out of Swedenborgian theology) believes that Jesus did not actually pay our sin debt. I base this on two of their principal doctrines:

"There are two essentials which constitute the church, and hence two principal things of doctrine — one, that the Lord's Human is Divine; the other, that love to the Lord and charity toward the neighbor constitute the church, and not faith separate from love and charity." It is by these two essential doctrines that conjunction with the Lord and salvation is effected. If one is unaware of these two essential doctrines of the New Church and yet has believed in one God and lived a good life, they will be taught this by angels after death.

From what I’ve read I understand that they believe Jesus’ soul was divine from eternity although he did not exist prior to being born of Mary. After his resurrection he put off the human body he inherited from Mary, and put on a human body from the Divine within Him, which is known in the New Church as the Divine Human.

During His life Jesus progressed towards God by gradually making the human body he inherited at birth one with the Divine... It was this progress towards unification, completed by the passion on the cross that is the means by which all of humanity was saved from hell.

Other names for The New Church include Swedenborgian, New Christian, and Church of the New Jerusalem. Swedenborgians accept the four Gospels of Matthew, Mark, Luke, John; and the Book of Revelation as divinely inspired canon of Scripture. Source: https://en.wikipedia.org/wiki/The_New_Church

If Jesus’ “progression towards unification” with the Divine is the means by which all of humanity is saved, and if all that is required is for people to repent, love God and live a good life, then there would be no need for Jesus to pay the entire debt of sin. The following Christianity Stack question is relevant to the Swedenborgian view of Jesus’ sacrificial death:

Many Christians believe that Jesus died to appease the anger of God. One reason for this is 1 John 2:2, which says: “And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world.” Propitiation basically means to appease the wrath of a god through an offering. How did Swedenborg interpret 1 John 2:2: "He is the propitiation for our sins"?

In response to this question, Lee Woofenden says:

Swedenborg was aware of, but rejected, the traditional philosophically-based interpretation of "propitiation" as meaning to appease the wrath of God the Father through the literal shedding of blood and death of the Son of God on the Cross. He goes on to explain why divine justice does not save one person due to the actions of another person (in this case, the Son of God)...

Swedenborg insists that although God does indeed forgive all of our sins out of pure love and mercy, the only way we can receive that forgiveness is to repent from our sins and live a new life of love and service to our fellow human beings, as Jesus Christ and the entire Bible command us to do... "propitiation" has to do with God "covering over" our sins, meaning forgiving them out of pure love and mercy—which forgiveness we receive when we repent from our sins and live a good life instead, as God commands us to do throughout the entire Bible, both Old Testament and New.

I could be wrong, but I get an impression that “The New Church” and those groups associated with Swedenborg, believe that “it wasn't required that Jesus' suffering was equal to or exceeded all the suffering of punishment that each one of us is due because he dealt away with the legal requirement, period, through the cross.”

If I have misunderstood and misrepresented anybody, I will apologise unreservedly. Please be aware I do not agree with the views expressed by The New Church or Swedenborg.

What is clear is that Swedenborgians do not believe that Jesus paid our sin debt.

There is one group that teaches its members that when they die physically, that is when they will pay for their own (individual) sins. Simple logic shows that this means they do not believe Jesus paid for their own (individual) sins.

They base this on their interpretation of Romans 6:7. This quote shows their teaching that Jesus has not paid for the sins of these ones:

“Judgment Day and Afterwards ...So, contrary to popular opinion, he will not judge persons on the basis of their past sins, many of which may have been committed in ignorance. The Bible explains that at death a person is set free or released from any sins he has committed. It says, ‘He who has died has been acquitted from his sin.’ (Romans 6:7) This means that when a person is resurrected he will be judged on the basis of what he does during Judgment Day, not on what he did before he died.” (Paradise book pp62-63, published in 1982)

It then goes on to state their teaching that Judgment Day is a one-thousand-year period following Armageddon. It is that doctrine of the basis for judgment being what all survivors of Armageddon and all resurrected ones will do during this still-future time, as stated in their ‘Paradise’ book, that prove they believe physical death cancels out a person’s personal sins. They take Romans 6:7 to mean physical death, and not spiritual death (dying to one’s sins and being spiritually ‘raised’ instantly, while living in the flesh.)

However, there is a caveat due to another doctrine about a tiny number of people who will go to heaven straight after death.

"Jesus knew that he was going to purchase these anointed ones with his own blood, so he fittingly referred to them collectively as his slave.” Watchtower, May 1, 1993, p.17

That group believes that Jesus paid for their sin debt as they are in the new covenant Jesus inaugurated by shedding his blood. However, this group only constitute a tiny percentage of members of this Jehovah’s Witness religion. That is why nearly all of the others (who are not in the new covenant) accept the teaching that they will pay off their own sin debt when they die physically. Those who do not die, but who survive Armageddon and live during the Millennium on earth will take that to be evidence of God’s favour, and an indication that they should be able to prove themselves worthy of everlasting life at the end of that thousand years.

I make no comment on their interpretation of Romans 6:7, nor of your citation of those other verses (Col 2:14, Romans 7:1-6 and Ephesians 2:14-16). That is because the question does not call for justification of how the groups you ask about view such verses. The one point I will repeat, for emphasis (because it is immensely significant) is that the Jehovah’s Witnesses believe there is no need for Jesus to pay for the sins of those who die before Armageddon, who will be resurrected on to a paradise earth afterwards, because their physical deaths supposedly paid for their personal sins. The clear statement they have published on this is (as above), “when a person is resurrected he will be judged on the basis of what he does during Judgment Day, not on what he did before he died”. Their view is that Judgment Day will last for one thousand years.