Sec. 3 of the 14th amendment mentions insurrection but doesn't explain how someone is known to be guilty of it. So if the Democrats claim someone is guilty of insurrection, apparently that is enough--no court trial needed to show that someone is actually guilty of the offense.
It's the Republican Party's fault--it was Republican members of Congress who drafted the 14th amendment and coerced enough Southern states to ratify it to get to the three-quarters mark.
You’re right about everything in your post.