“section 5 clarifies who can enforce this provision...”
Section 5 doesn’t prevent a court from enforcing Section 1 and there is no reason why it would prevent a court from trying to enforce Section 3.
A court in New Mexico has barred (and tossed out) a J6 defendant from public office.
You cite the only example in history, so far, where this worked, and I would suggest that that person did not appeal. If he had, he would have won because higher courts ruled in favor of both MTG and Madison Cawthorne in exactly the same cases.