TLDR version is that Amendment 14 Section 3 says if you were involved in an attempt to overthrow the government you no longer are allowed to hold public office.

Section 3 Disqualification from Holding Office No person shall be a Senator or Representative in Congress, or elector of President and Vice-President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may by a vote of two-thirds of each House, remove such disability.

It only matters if anyone does something about it. Really there should be a few traitors kicked outta congress as well but they haven’t been.

I think the trick is going to be, based on the other guy who got disqualified for 1/6, is that someone actually has to challenge the nomination. It’s not something that happens automatically.

https://abcnews.go.com/Politics/judge-removes-local-official-engaging-jan-insurrection/story?id=89463597

“The decision came in a lawsuit brought by a group of New Mexico residents represented by the government accountability group Citizens for Responsibility and Ethics in Washington (CREW) and other lawyers.”