When a separatist region WINS the civil war - generally corroborated afterwards by being recognized by other sovereign states - then it is a sovereign nation.
Regards,
Well, that also depends. The South seceded (as whole states, not “separatist regions”) and no war immediately started, so at least for a time, though the North disagreed, they were effectively ruling themselves and at peace with the rest of the US, and they were recognized by at least some countries, because they obtained foreign allies.
And prior to the “Civil War” there was no established legal doctrine that states, who had voluntarily entered into a union as sovereign states, could not voluntarily leave the union as sovereign states. Only the resolution of the war resulted in a settlement of that question for practical purposes.