Now, regarding the Papal endorsement of St. Augustine's opinion in the period when he taught BOD, it can be argued that the Pope may not necessarily have agreed with everything St. Augustine said, but approved a particular opinion within his writings. By way of analogy, when the Popes approved St. Athanasius' Creed, they didn't approve everything he ever wrote, however orthodox all those writings may be. They did endorse that particular Creed he composed, especially at Florence.

We assert without hesitation (on the authority of the holy fathers Augustine and Ambrose) 

https://catholicism.org/baptism-of-desire-its-origin-and-abandonment-in-the-thought-of-saint-augustine.html

Everyone should read this terrific article.

St. Augustine: “If you wish to be a Catholic, do not venture to believe, to say, or to teach that ‘they whom the Lord has predestinated for baptism can be snatched away from his predestination, or die before that has been accomplished in them which the Almighty has predestined.’ There is in such a dogma more power than I can tell assigned to chances in opposition to the power of God, by the occurrence of which casualties that which He has predestinated is not permitted to come to pass. It is hardly necessary to spend time or earnest words in cautioning the man who takes up with this error against the absolute vortex of confusion into which it will absorb him, when I shall sufficiently meet the case if I briefly warn the prudent man who is ready to receive correction against the threatening mischief.” (On the Soul and Its Origin 3, 13)

https://catholicism.org/baptism-of-desire-its-origin-and-abandonment-in-the-thought-of-saint-augustine.html

Everyone should read this terrific article.

From the time of Saint Augustine to that of Saint Bernard (+1153) in the twelfth century, I could discover no doctor of the Church who affirmed a belief in baptism of desire. Father Pfeiffer asserts in his article that there are “a host of other saints and Doctors before and after Aquinas,” who taught baptism of desire. “After Aquinas?” Granted. “Before?” With Augustine’s recantation (full text supplied later on), I do not know of any, other than Saint Bernard.

Rev. Father Jean Marc Rulleau in his booklet, Baptism of Desire: A Patristic Commentary, attempts to defend the same point as Father Pfeiffer concerning the fathers’ approval of baptism of desire, but he provides only the flimsiest of evidence from the fathers. He maintains that Saint Cyprian (+258) believed in baptism of desire — not for catechumens (Cyprian does not raise that question), but for those converts who he thought were invalidly baptized in a heretical sect. The question Cyprian raised was this: if they converted and were received into the Church without being re-baptized, could they be saved? He believed that they could be saved.

I agree with Father Rulleau that this opinion could be translated into a baptism of desire. In any event, the historical fact is that Saint Cyprian refused to accept Pope Stephen’s correction (including the threat of excommunication in case of non-compliance) of his teaching concerning the invalidity of baptisms in heretical sects that used the correct matter and form. He even summoned a council at Carthage in 256 to gather the support of a synod of African bishops. The decision of that council, to which Cyprian acquiesced, was that the question of re-baptizing converted heretics was a disciplinary issue reserved for the local bishop. In this, he had what appears to be the support of the eastern Catholic bishops whom he had also solicited. In a letter he wrote to one Jubaianus, the bishop of Carthage explained that he makes no laws for others, but retains his own liberty. (Epp. lxx, lxxi, lxxii) Then, again, in a later letter to one Pompeius, to whom he sent his work, De Bono Patientiae, he is virulent in his attack on Pope’s Stephen’s orthodoxy. Pompeius had asked for a copy of Stephen’s decree. “As you read it,” Cyprian writes, “you will note his error more and more clearly: in approving the baptism of all the heresies, he has heaped into his own breast the sins of all of them; a fine tradition indeed! What blindness of mind, what depravity!” (See New Advent’s 1917 Catholic Encyclopedia on Saint Cyprian.)  In the end, after the martyrdom of Saint Cyprian and under the pontificate of Pope Sixtus II, the Church in Carthage fell in line with the pope.

Point being: If the Bishop of Carthage was wrong on the bigger question, speaking and writing in ignorant opposition to the apostolic tradition (and, be it noted, following the opinion of the heretic Tertullian on the subject) and questioning the pope’s authority, are we to hold that he was correctly handing on traditional teaching on a subsidiary issue related to the original error? Reading the insulting language Cyprian employs against the pope in his letter to Pompeius one can understand why Saint Augustine, with great respect and prudence, would say over a century later, in his treatise De Baptismo, that Bishop Cyprian had atoned for his “excess” by his martyrdom.

Father Francois Laisney, in a letter written to me in 1999 on this issue, labored much to convince me that Saint Cyprian favored baptism of desire. Regarding those converted heretics who were received back into the Church by the western bishops and the head of the Church himself without being rebaptized, he proved his point. But these converts were in a different category than catechumens — after all, they were accepted as members of the Church by the pope, and Cyprian himself, at least in council, was not denying the pope the right to admit these converts without rebaptizing them. Remember, in the previously-cited letter to Jubaianus he was arguing that this decision should be left to each individual bishop. His contention, therefore, if one looks at the logic of the actual argument and not his excessive vitriol, was not that the “deposit of faith” was being compromised by Pope Stephen, but that, for certainty sake, when the validity of heretical baptisms was questionable (as it was in his mind) the matter fell to one of discipline. To quote Saint Cyprian: “God is powerful in His mercy to give forgiveness also to those who were admitted into the Church in simplicity [of heart] and who died in the Church and not to separate them from the gifts of the Church” (Letter to Jubaianus, n. 23, Patrologia Latina 3, 1125). I put the emphasis on “died in the Church” to prove my point. If Saint Cyprian definitely believed that the Faith itself was being compromised, and that to accept the validity of heretical baptisms was itself “heretical,” then he would not have said that the deceased converts, who were not rebaptized, “died in the Church.” If Fathers Rulleau and Laisney wish to believe that Saint Cyprian was transmitting an apostolic tradition concerning baptism of desire, fine; but they certainly should not insist that fellow Catholics are obligated to believe that. They should also take note that Saint Augustine did not cite Cyprian as an authority when he first proposed baptism of desire as his own personal opinion.