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A judgment of the internal forum is required in order to conclude that one has committed the public sin of formal heresy.

I think you've just exposed your error here.  Even the CHURCH does not judge the internal forum:  De internis Ecclesia non judicat.  You cannot make a judgment about the internal forum, nor can the Church.  Only God can.

Pertinacity has nothing to do with "sincerity".  Pertinacity is a matter of the public forum and basically means that the person adheres to the doctrine and didn't simply mis-speak, fumble, or act from ignorance.  If they know the Church teaches the contrary and teach something and stick to it (as Ratzinger did with his doctrine contradicting Florence), that's all the pertinacity that's require to establish manifest heresy.  In fact, as I stated, Bergoglio, a bumbling fool in some respects compared to Ratzinger, is more likely to have simply been ignorant that he's contradicting Church teaching.

Pertinacious Manifest Heresy has absolutely nothing to do with the internal forum.  Corollary is that someone could be a heretic in the internal forum but does not lose office or membership in the Church.

Basically the opposite of pertinacity is when someone, say, has a slip of the tongue or a "brain fart" or just honestly believed the Church teaches what he said and then shows the willingness to be corrected immediately.  But if someone persists in teaching something, where it's clearly not just some kind of temporary slip-up, that's all that's required for pertinacity.  Where it gets complex is when something isn't an obvious contradiction of Church dogma but is merely disputed.  "That's heretical.  No it's not.  Yes it is." ... due to some disagreement about the argument, where something is derived from dogma rather than having been directly declared.  But both Ratzinger and Bergoglio (and Wojtyla for that matter) DIRECTLY contradict the dogmatic teaching of Florence, so that's not in play here.

Non-pertinacious heretics are easily discernible in the public / external forum.  "Hey, that's heretical."  "Really?"  "Yes, here's what the Church teaches."  "Oh, my mistake.  I change my mind."

We have an entire thread about it here that beat Marshall to it by a day ...
https://www.cathinfo.com/crisis-in-the-church/jaccuse/msg941376/

Not sure why it's explosive.  +Vigano has already said Bergoglio is not the pope, arguing before from vitium consensus.  What's different this time is that +Vigano also articulates the principle that heretics cannot become popes and that Bergoglio is not a pope on those grounds as well, even citing cuм ex Apostolatus.  Why that's important is that it puts him just a baby step away from holding Montini-Ratizinger to also be non-popes ... and in fact implicitly does so.

+Vigano affirms that the Church cannot teach error and then states that Vatican II taught error and is not Catholic Magisterium.

Thank you for the link. I do not have time to read all threads, so that helps :-).

No, it's not true that the Church can judge "internal" actions.  Again, De internis Ecclesia non judicat..  If something is manifest externally, then it's external and in the external forum.

Pertinacious Manifest heresy is discernible in the external forum.  You're just playing this wishful-thinking game of attempting to salvage Ratzinger while getting rid of Bergoglio because that's what you want the outcome to be.  So you engage in all these gymnastics and contortions to claim that Bergoglio really means his heresies while Ratzinger didn't.  Ratzinger new very well that he was contradicting the Council of Florence, and knew it much better than Bergoglio did.