Doesn't the use of "insurgents" imply that "combinations too powerful to be suppressed by the ordinary course of judicial proceedings" is the same as an insurrection?
Whatever the implications of the 1790 law, the 1861 law made the situation clear.
The July 13, 1861 Act of Congress, under which authority Pres. Lincoln shortly after declared the people of the Southern States in insurrection, says the "insurrectionists" were defending the "combinations" which had interposed between the US Govt. and the States, etc. Interestingly, this act was predicated principally on the War Powers of the US Govt. versus the treason clause of the Constitution.. as it included in punishment for insurrection etc. the confiscation of property and imprisonment. The amnesty declared by Lincoln etc. on taking the oath would relieve most against the confiscatory elements of the law...
However, the Confederate States of America, only recognized and continued to the use of the laws of the USA up to November, 1860, and declared attempts by any but the CSA to enforce them, or any US law passed since their secessions, was an invasion... Once the CSA was crushed out, in October, 1865, Gen. Lee took the oath of allegiance recognizing the laws of the Union, and the emancipation, etc., established since the war commenced...
But from 1861 the CSA constitution also included a definition of treason as levying war against the Confederate States, etc. Each State also had its own constitutional or legal provisions regarding treason too.
Everybody knew the punishment of treason was ultimately death. The question for those in the South was to whom would one adhere; because to do nothing was to potentially be declared in insurrection against the USA, the CSA, or one's State in turn or even simultaneously...
I have also seen it said (I think Justice Story in the 1830s) that an individual State cannot have jurisdiction or "cognizance" of treason against the United States (levying war against "them"), while any treason against a State (levying war against "it") which overthrew the State government without impeding the action of of the federal laws therein (like a "combination" would), might not be recognized as treason against the United States...