Cite where Bellarmine states that a "discretionary judgment" is essential to rendering the heresy "manifest". You try to cobble together a narrative from this, but in treating the subject of a heretical Pope Bellarmine explicitly states that it's only because he's already lost the pontificate that he can be judged and punished.
He can only be judged and punished, because being “judged and punishment” is a perfect judgment, which is not permitted while he remains pope. If a pope is suspect of heresy, or accused of heresy, what is permitted is that a council gather to investigate and discuss the case. If the bishops find that he is guilty, they can declare him outside the Church and then “judge and punish” him (in a manner proper to a superior).
That is Bellarmine’s position, and it is confirmed by his treatment of the case of Pope Marcellinus, who was accused of offering incense to the idols, which was considered a public act of apostasy at the time. Read carefully what Bellarmine wrote about this case. It comes immediately after he discusses the difference between a perfect judgment and a discretionary judgment:
“The example of Marcellinus, who in the Council of Sinvessano was condemned by the bishops and deposed. I respond: Marcellinus was accused of an act of infidelity, in which case a Council can discuss the case of the Pope, and if they were to discover that he really was an infidel, the Council can declare him outside the Church and thus condemn him.”
The council is not gathered simply to declare him deposed. It must first investigate and discuss the case, and only if he is found to be guilty (which requires a judgment), does it legitimately declare him to be separated from the Church.
Another teaching of Bellarmine worth considering is found in his treatment of the case of Pope Liberius. Setting aside the fact that Bellarmine was wrong in believing that Liberius lost the pontificate, what he says about the case is of interesting since it helps to show what his true position is.
“Then two years later came the lapse of Liberius, of which we have spoken above. Then indeed the Roman clergy, stripping Liberius of his pontifical dignity, went over to Felix, whom they knew to be a Catholic. From that time, Felix began to be the true Pontiff. For although Liberius was not a heretic, nevertheless he was considered one, on account of the peace he made with the Arians, and by that presumption the pontificate could rightly be taken from him.”
Because Liberius was considered (which is a judgment) to be a heretic, Bellarmine said "the pontificate could rightly be taken from him" and that the Roman clergy “stripped Liberius of his pontifical dignity.” You cannot take from someone what they no longer possess, nor could the Roman clergy strip Liberius of his pontifical dignity, if he had already lost his pontificate dignity.
Now, the Church cannot directly strip of pope of his pontificate, but it can do so indirectly by first determining that he is a heretic, and then legitimately declaring him deposed. That's what Bellarmine meant. And if the Church has not taken such actions, the faithful must remain subject to him and obeyed him in all legitimate commands, as Bellarmine teaches.