Bellarmine says at that point, deposition is ipso facto; Cajetan/JST say a second Church action must declare God has deposed the pope).
No, Sean. If you actually read Bellarmine, his entire reason for rejecting Cajetan is that the Church cannot render a judgment regarding a sitting Pope, so the deposition must happen
a priori to any such judgment. Every theologian who's ever read Bellarmine has read it that way, which is the obvious sense of his text. S&S and you are playing games with the fact that Bellarmine says the Church has to judge heresy whereas Cajetan says the Church has to declare him deposed, but the core principle in the dispute is whether deposition occurs prior to or after the Church's judgment of deposition. You're playing with nonsensical semantics.
Bellarmine is clearly right. If the Pope remains the Pope until the judgment is rendered, you're violating the principle of
suprema sedes a nemine judicatur. In fact, the contrary was officially condemned later at Vatican I, which dogmatically backed the notion of Conciliarism on grounds that undermine Cajetan and SJT's position. So the Cajetan/JST position is implicitly heretical after Vatican I. Father Kramer does a good job of pointing this out.
Now, in St. Robert, and in the citation from Pope St. Celestine, the seeds of sedeprivationism and sedeimpoundism are there. St. Robert cites Pope St. Celestine on the case of Nestorius, where there's a distinction made between his official removal from office (the material aspect) and his being impounded or deprived of authority. So between the time that Nestorius began preaching heresy (became a manifest heretic) and the time he was officially removed from office, Nestorius was deprived of all authority. In other words, he was formally deposed but not materially deposed yet. Pope St. Celestine's teaching, followed by St. Robert Bellarmine, was basically sedeprivationism or sedeimpoundism in a nutshell. So it's the inability of S&S to understand this distinction that causes them to blunder.
Bellarmine: Deposition occurs
a priori to a declaration by the Church.
Cajetan/SJT: Deposition doesn't occur until the judgment of the Church.
Cajetan/SJT position is implicitly heretical since Vatican I.
Yet Bellarmine distinguishes between the official removal and the loss of authority, which is sedeprivationism before the term was coined ... and also sedeimpoundism.