That implies that succession was (and still is) perfectly legal, so neither the act of succession nor defending the states that had succeeded can be considered traitorous.

I have no idea how you make this particular logical leap. When people say the war was about slavery or the war was about states' rights, they're talking about motive, the reason the South had for seceding, not the act of secession itself.

As far as secession itself goes, that matter was adjudicated on the battlefield and again in the courts. In Texas v. White, 1869, the Supreme Court found that secession is unconstitutional. There's really nothing more to say.

Treason is the only crime defined in the United States Constitution. One of the ways that a person engages in treason against the United States is in levying war against them.

In this case, South Carolina started the war by opening fire on a military installation of the United States. In April of 1861, elements of organized military forces of the state of South Carolina opened fire on a military installation of the United States. In international law, the act of one military force intentionally engaging or firing upon a military force against which on is in rebellion or of a different nation state is an act of war.

Ten other states doubled down on South Carolina's rebellion. Those states organized a national government. That national government raised armies. Those armies fought armies that were raised by the United States in order to suppress the insurrection.