Which is true, but not a great argument in support of no evidence required.

A majority of U.S. Senators voted "guilty"

I mean, sure - but so what?

No one in this thread has suggested that no evidence is required. I responded with the Senate vote showing that evidence has been presented and similar evidence will be presented again in the civil cases. I consider the Senate impeachment trial to be a serious undertaking, and while different than a state civil trial there are some similarities in evidence presentation and arguments. Many Senators found evidence of insurrection. I would expect many state courts to find the same.

The OP 126 page law review article says "in principle: Section Three's disqualification rule may and must be followed'applied, honored, obeyed, enforced, carried out'by anyone whose job it is to figure out whether someone is legally qualified to office, just as with any of the Constitution's other qualifications". Whatever the Secretary of State decides, a civil lawsuit will follow, and the issue will be decided in a state court, with all of the normal appeals all the way to the Supreme Court.

The Sweep and Force of Section Three, 14 Aug 2023
"Section Three is self-executing, operating as an immediate disqualification from office, without the need for additional action by Congress. It can and should be enforced by every official, state or federal, who judges qualifications."
SSRN: Research paper