I have no doubt you believe the CMRI has refuted Billuart.
😕
There's nothing in there from CMRI; it's simply a translation of Bellarmine. So I have no doubt that you didn't even bother to click the link before denouncing it, since you rule out beforehand any arguments against your predetermined conclusions.
Despite your use of an obnoxiously large font, Billuart's position has to do with ordinary lower-level prelates, and not popes. Take the case of Cardinal Cushing, for instance. He was clearly a manifest heretic. But the faithful are not obliged to avoid him, and he can retain a certain amount of jurisdiction and continue to exercise jurisdiction, though color of title, at the very least, until he would be deposed by Rome.
But the papacy is different:
1) because Popes receive their authority from Christ and
2) no one can judge or denounce or depose him
Billuart (and Pope Martin) were referring to jurisdiction with regard to receiving the Sacraments. Thus, although Cushing was a manifest heretic, the priests appointed by Cushing would still retain jurisdiction to hear Confessions, for instance. That's all that was in that text that you continue to misapply.
In his closing paragraph, Billuart admits that all that went before does not necessarily apply to the papacy (something you ignore), but then states that he believes God would continue to supply jurisdiction for the good of the Church. But this is along the lines of the "color of title" position held by the sedevacantists, and would be limited to things like making appointments or jurisdiction for the reception of the Sacraments.