I will attempt to explain how I am reading this. I am having trouble being succinct. Please overlook it.:
Often translators combine multiple items as 'Sin' (in Greek Koine) when they are separate things. This was not a problem when readers understood Torah, but people today don't know Torah usually. These different items called 'Sin' must become differentiated again to understand where the concept of original sin is from and what it is supposed to mean. If you do something bad you bring trouble (iniquity) upon your descendants, but that often is translated as sin, confusing people. Its iniquity. Multiple things are translated into the Greek Koine using the same word 'sin', but that doesn't mean they are the same.
The trouble (iniquity) of being a human is the original 'Original sin'. It is our tendency to sin. It is our nature. These are the things that Christ's death atones for. Contrarily we have to repent from vicious acts and undo them to the best of our ability, and they aren't atoned by sacrifice. You can't hurt someone and fix it by killing a goat. This can be seen by reading the list of sacrifices in Leviticus and noting what they are for, especially the sacrifice of the Red Heifer, which Jesus gets associated with. People still must do right and try to undo their harms. Then their community and God can forgive them. That doesn't change with the cross.
NT writers imply that what Jews do with ritual, with food, with various things is attempt to circumcise the heart. That is part of their law, and their law says so.
Even so until that happens they must function with hearts that have pride built in, but keeping the law atones for it in the community. They take kiddish, train hard, keep festivals and do many things to make real what is symbolized in their flesh. So they deal with their human tendency to err by following the law, but gentiles do not.
Gentiles have a simple Noahic covenant of peace. You don't kill me, and I don't kill you. We live in peace and thus the world is not destroyed. Jewish law goes beyond that with its atonement, community sacrifices, meditations, laments, festivals, justice system, forgiveness and laws.
The most important thing is that atonement with God is also atonement between Christians. Jesus teaches that if you forgive, you are forgiven. You cannot exclude other Christians and judge them while expecting God to ignore your own humanity. That is not how things work. That is not atonement.
There is forgiveness beyond original sin. This is where evil actions are forgiven, but they are not atoned through sacrifice. They're atoned when the person repents and is forgiven by others. If a Christian commits theft, they ought to repay if they are able. If they are a soldier, they ought to be as just as possible and not extort people...etc and so on. They can't just do whatever. The atonement is between God and between Christians a group effort, and forgiveness above and beyond that is, too.