"The pope's status" is derivative of his manifest actions and statements—"automatically," "immediately," "without need for any further declaration," etc.
We certainly have the right and obligation to judge manifest outrages against the Faith.
We have no right or obligation to depose a Pope, but that is irrelevant because a heretic deposes himself.
The popes' status is by law, established upon him accepting his election, once he does that, the law states that:
"the man
elected is instantly the true Pope, and he acquires and can exercise full and absolute jurisdiction over the whole world". So according to the law, if his status is a derivative of anything, then his status is derived from the pope accepting his election, and not from the approval of his subjects or speculations of some of the Fathers of the Church.
I absolutely agree that, as you said;
"we certainly have the right and obligation to judge manifest outrages against the Faith" - to which I add that we have this obligation no matter who does it, or where it comes from. The reason that we have this obligation is to pray for the offender because to die in that sin means eternal punishment, but also so that we do not lose the faith ourselves, and also in order to keep, grow and persevere in the faith, but this obligation does not exist in order to decide the status of popes.
I also agree we have no right or obligation to depose a pope, yet if his heresies cause him to self depose, we can never know it without a declaration from a future pope stating as much, lest, like Ibranyi, we gravely err in claiming true popes are not popes at all.
So there is much we agree on.