Section 3 of the 14th Amendment to the Constitution of the United States reads as follows:
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.
While it does not make clear precisely what action by what authority affirms the “disability” from a person who betrayed their oath from ever holding office again, it is significant that the Constitution specifies that such a person can only hold office—at any level of government, anywhere within the US—if two-thirds of both houses of the United States Congress vote to grant them special permission.
Respond to Insurrectionists barred from public office by US Constitution