The Sede-Vacantists totally misrepresent the "pious opinion" of Cardinal St. Robert Bellarmine. St. Robert never said, of Pope Honorius or Pope John XXIII, "if he fell into heresy, then he was never Pope in the first place", or any other such modern sedevacantist absurdity; for that holy Doctor knew, as all Theologians have always taught, that universal acceptance is a sign and infallible effect of a valid election. The election of Pope Francis being therefore recognized by the Teaching Church (even Cardinal Burke has frankly stated that, carefully considering everything, he prays for Pope Francis in the Mass as Pope, and not lightly, knowing that is profession of communion with him; as Pope Benedict XIV taught in Ex Quo, "it suffices Us to be able to state that a commemoration of the supreme pontiff and prayers offered for him during the sacrifice of the Mass is considered, and really is, an affirmative indication which recognizes him as the head of the Church, the vicar of Christ, and the successor of blessed Peter, and is the profession of a mind and will which firmly espouses Catholic unity. This was rightly noticed by Christianus Lupus in his work on the Councils: “This commemoration is the chief and most glorious form of communion” (tome 4, p. 422, Brussels edition). This view is not merely approved by the authority of Ivo of Flaviniaca who writes: “Whosoever does not pronounce the name of the Apostolic one in the canon for whatever reason should realize that he is separated from the communion of the whole world” (Chronicle, p. 228); or by the authority of the famous Alcuin: “It is generally agreed that those who do not for any reason recall the memory of the Apostolic pontiff in the course of the sacred mysteries according to custom are, as the blessed Pelagius teaches, separated from the communion of the entire world” (de Divinis Officiis, bk. 1, chap. 12). https://www.papalencyclicals.net/ben14/b14exquo.htm), it is certain that Pope Benedict XVI resigned and that Pope Francis is the validly elected Successor of St. Peter. This also means all who do not commemorate Pope Francis are now schismatics. That's just the way the Church works - the Teaching Church, the Ecclesia Docens, acknowledges a valid election - all the faithful are bound to do so.

What St. Robert said and proved, just like he would do today, is that many of the false accusations of heresy, were not heresy at all, or were based on misunderstandings. Most Catholics don't even know what Monothelitism is or all the theological intricacies it involved. And yet supposedly laity or clerics, by their own private judgment contrary to the judgment of the teaching Church, can supposedly declare a Pope to be a manifest formal heretic and pertinacious on their own private presumptions of pertinacity? That's the send of sanity and Christianity. No Pope would be safe, and that's why you have sedes all over the place lapsing into Orthodoxy, Old Catholicism, or general secularist worldliness, leaving the Church; and so many other disorders one observes in the sede-vacantist movement. 

Cardinal Billot: "I said under the supposition of the hypothesis. But the fact that the hypothesis itself is a mere hypothesis, never reducible to an act, appears far more probable, according to Luke 22:32: But I have prayed for thee, that thy faith not fail; and thou being once converted, confirm thy brethren. For the voice of all Tradition says we must understand this verse to refer to Peter and his successors in perpetuity ... For Innocent had said earlier: “If I were not made firm in the faith, how could I strengthen others in the faith? That is what is recognized as pertaining especially to my office, as the Lord witnesses: I have prayed for thee, Peter, that thy faith not fail; and thou being once converted, confirm thy brethren. He prayed and He brought it to pass, since He was heard in all things out of reverence for Him. And therefore the faith of the apostolic see has never failed in any disturbance, but has always remained whole and unimpaired in order that the privilege of Peter should persist unshaken.” Consequently, that statement is rather in opposition to adversaries, unless they should say that by it Innocent actually means he can sometimes lack that which the Lord procured for Peter as necessary for the office to which he appointed him...

But whatever you finally think about the possibility or impossibility of the aforementioned hypothesis, at least one point must be maintained as completely unshaken and firmly placed beyond all doubt: the adherence alone of the universal Church will always be of itself an infallible sign of the legitimacy of the person of the Pontiff, and, what is more, even of the existence of all the conditions requisite for legitimacy itself. One need not fetch from afar proof of this claim. The reason is that it is taken immediately from the infallible promise of Christ and from providence. The gates of hell shall not prevail against it, and Behold I am with you all days. 

...By all means God can permit that at some time or other the vacancy of the see be extended for a considerable time. He can also allow a doubt to arise about the legitimacy of one or another man elected. But He cannot permit the entire Church to receive someone as pontiff who is not a true and legitimate [pope]. Therefore, from the time he has been accepted and joined to the Church as the head to the body, we cannot further consider the question of a possible mistake in the election or of a [possible] deficiency of any condition whatsoever necessary for legitimacy, because the aforementioned adherence of the Church radically heals the mistake in the election and infallibly indicates the existence of all requisite conditions. And let this be an incidental remark against those who want to join in giving a respectable appearance to the undoubted schismatic efforts made in the time of Alexander VI on the ground that they were made by one who persisted in saying that the most certain evidence in the matter of the heretical state of Alexander VI had to be disclosed in a general Council. However, so as to forego at the present moment other arguments whereby this opinion of his could be easily refuted, this one [argument] alone is sufficient: It is certainly well known that in the time in which Savanarola was writing his letters to princes, all Christendom adhered to and obeyed Alexander as the true pontiff. Therefore, by that fact, Alexander was not a false pontiff. Therefore he was not a heretic..."

All this contradicts the first commandment of the new sedevacantist religion, which basically has become reduced to: "There is no Pope. I shall have no Popes before me. I shall take the Lord's Name in vain, and say He has failed in His Promise to His Church." Sede-ism is not even remotely Catholicism, but is pure private judgment doctrine-defying, Hierarchy-rejecting, Papal-perpetual-successors-dogma-denying Protestantism.

He believed the Church must be involved in the process of making at least a declaration of the fact of tge pope’s heresy (with the matter of the ipso facto loss of office beginning only from that time).

This^^^^^

All the Catholic bishops have already separated themselves from Francis and the Conciliar hierarchy.  The Church has spoken.

QFT

It’s interesting that the Novus Ordo XavierSem recognizes that traditional Catholics who continue to worship and believe the doctrine of the Apostles are in a different religion from that of the Conciliar Church.  Yes, it’s called the Catholic Church.

Sedes deny Apostolic doctrine right from Apostolicity itself. The Catholic Church is a universal, visible, Hierarchical Church, consisting of, and identified by, the Pope, and the Bishops appointed by him. This is clearly explained by Pope St. Pius X and Pope Ven. Pius XII. 

Catechism of Pope St. Pius X: "43 Q. Of whom is the Teaching Church composed?
A. The Teaching Church is composed of all the Bishops, with the Roman Pontiff at their head, be they dispersed throughout the world or assembled together in Council ...

48 Q. Does the power possessed by the members of the Hierarchy come from the people?
A. The power possessed by the Hierarchy does not come from the people, and it would be heresy to say it did: it comes solely from God.
49 Q. To whom does the exercise of this power belong?
A. The exercise of this power belongs solely to the Hierarchy, that is, to the Pope and to the Bishops subordinate to him." [Ninth Article of the Creed]

Rev. Father Dom Gueranger: "Rome was, more evidently than ever, the sole source of pastoral power.

We, then, both priests and people, have a right to know whence our pastors have received their power. From whose hand have they received the keys? If their mission come from the apostolic see, let us honour and obey them, for they are sent to us by Jesus Christ, who has invested them, through Peter, with His own authority. If they claim our obedience without having been sent by the bishop of Rome, we must refuse to receive them, for they are not acknowledged by Christ as His ministers. The holy anointing may have conferred on them the sacred character of the episcopate: it matters not; they must be as aliens to us, for they have not been sent, they are not pastors.
Thus it is that the divine Founder of the Church, who willed that she should be a city seated on a mountain, gave her visibility; it was an essential requisite; for since all were called to enter her pale, all must be able to see her. But He was not satisfied with this. He moreover willed that the spiritual power exercised by ‘her pastors should come from a visible source, so that the faithful might have a sure means of verifying the claims of those who were to guide them in His name. Our Lord (we say it reverently) owed this to us; for, on the last day, He will not receive us as His children, unless we shall have been members of His Church, and have lived in union with Him by the ministry of pastors lawfully constituted." https://reginamag.com/saint-peters-chair-at-antioch/

In no case has a vacant see per se constituted a defection.  In particular, the vacancy of the Holy See does not constitute a defection.  And if the Holy See has not defected then neither has the Catholic Church defected.

But if Bergoglio is pope, then it has defected.