While I agree with you in principle I think you would find that the courts would rule in the favor of the Senator.
If they can find the right to kill a child in its mother’s womb in the constitution finding the right for a senator to slander a judge in the during the process of the confirmation hearings is like finding rotten apples in a orchard in August.
Things are changing. What we have seen in the past was a sort of nullification. There just was no point bringing charges for crimes of a political nature in DC for obvious reasons. But there are ways to shift the jurisdiction. Let’s say the polygraph fraud was in Maryland. (Sure, Md is not much better but I wonder what a jury in Rehoboth Beach would look like,) Graham is pretty pissed and Grassley is extremely pissed. I would not want to have two US Senators pissed of at me.