Do some research about its intent.
Thete's nothing to research. The clause is quite clear...
No state shall enter into any Treaty, Alliance, or Confederation
No state shall, without the Consent of Congress .... enter into any Agreement or Compact with another State
The south could not form their own confederacy without violating Article I, Section 10 of the U.S. Constitution.
The north could have sought legal redress; though given the circumstances where the south abandoned the constraints of the Constitution, would have no doubt been fruitless. But then the south, as heartless and stupid as they were, gave Lincoln a military option when the Confederacy declared war by firing upon U.S. military inside a U.S. fort.