Reading through the actual brief:

if Section 3’s disqualification were fully self-enforcing, there would have been no reason for Congress to state expressly in § 2383 that a conviction for insurrection would result in disqualification from holding certain offices. Under Baude and Paulsen’s view, Section 3 would already have automatically barred such individuals from office even before conviction, and certainly would have done so after a conviction.

Yes. Yes, Section 3 already did bar such individuals from holding office. There was no reason for Congress to expressly state that prohibition in §2383.