The war was primarily about slavery, but more importantly the attempt from Southern States to codify the legality of slave-catchers in Northern States;

A specific tl;dr is slaves in the South increasingly were able to escape North; as they got to states where they were people, not property, they had all the inalienable rights of free men -- this meant that the state they escaped from could not compel them to return legally.

That did not stop them from trying -- resulting in kidnapping and clashes between local security forces (anything from port authority to sheriffs to the local militia) and slave catchers were becoming increasingly common. The South had one simple ultimatum -- all slaves were to be considered property unless explicitly freed, no matter where they were in the US. They would not budge on this, at all, which pushed Northerners to continue to exert their (at the time) right to secure their state and refuse to work out a 'compromise' federally that left them with less power.

This, along with the thought among the South that just threatening to secede would be enough to to get them to comply (they erroneously thought they contributed more economically and militarily to the US than the North did, so they thought the US would collapse without them), and then the North basically said "fucking do it, pussies." With the federal government really upset with both parties for refusing to compromise on, you know, the definition of a person.

After the South was defeated so badly that their already poor socioeconomics were simply worse than developing colonies at the time there was a compromise on slavery -- the 14th bans slavery except as a punishment for a crime (which is why the modern day south has roughly double the number of inmates as the former North, and also why red states now tend to have a significantly higher non-white prison population than other states).

The federal government also reasserted its dominance in matters related to interstate justice by establishing the first federal prisons shortly after the war, but this is widely considered to be just a way to cash in on federally legal slaves. Officially the federal government handles people that commit a crime in one state and then leave to another state if the law is also a federal crime, like murder; but it is still within each state to recognize out of state warrants for crimes that do not have a federal counterpart, and to that end the federal government does not interfere with those matters (possibly in any way, as in a state cannot compel another to accept a warrant, but the matter at hand, one state sending agents to another to arrest someone without permission of the host state hasn't been tried in a very long time.)

If there is precedence on the matter, it would be in SCOTUS' wheelhouse as, as far as I'm aware, there are no laws at the federal level stopping this -- and with SCOTUS' current makeup being close to that before the civil war, I wouldn't put it past them to basically force the issue into being legal with no recourse, which may result in direct interstate violence.