The supreme authority given to St Peter was clearly enunciated in the following:
Vatican I, Pastor Aeternus, Chapter 4:
“Therefore, such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable.”
Vatican II, Lumen Gentium 25:
“And therefore his definitions, of themselves, and not from the consent of the Church, are justly styled irreformable, since they are pronounced with the assistance of the Holy Spirit, promised to him in blessed Peter, and therefore they need no approval of other, nor do they allow an appeal to any other judgment.”
That expresses finality with no possibility of a contrary supposition, which some try to limit to the approval of others. That’s their problem. The Holy Spirit protects His Pope, and thus His Church, from teaching error in doctrine.
Bishop Gasser at Vatican I, working from the citation of Bossuet precisely on the question of papal authority and finality on doctrine and dogma gave reality, as Fr James T. O’Connor cites:
“Bishop Gasser argues that it would be impossible for the successor of Peter to fulfill his task of confirming the other bishops in the faith if a permanent guarantee of inerrancy had not been given to those who would succeed Peter in his Chair. It is a gift that cannot be dependant on the consent of the other bishops since such a consent would ultimately nullify the special duty of the primate to strengthen the others when their own faith was weak.” The Gift of Infallibility, Ignatius 2005, p 26].