Hey, you asked.
But none of that happened until long after secessionists provoked war by illegally seizing dozens of Federal properties (forts, ships, arsenals, mints, etc.), started war at Fort Sumter, formally declared war (May 6, 1861), and waged civil war, including in Union states & territories, eventually refusing to stop fighting on any terms better than Unconditional Surrender.
The US Constitution nowhere requires that people at war with the United States must keep their seats in Congress even after they walked out!!
Indeed, for such people the Constitution provides us a clear definition of the word "treason".