So you’re not talking about Apostolic Succession either.
Not unless Peter was an Apostle and the bishop of Rome his successor.
I am not going to get into a semantics game on this with you and this will be my last response to you.
Whether they are or not by the Catholic Church is not of much importance to me. But it seems apparent the petrine ministry and apostolic succession should be considered related in this sense:
Peter was an apostle and the bishop of Rome. And the bishop of Rome is believed to be his successor.

Peter and apostolic succession.
Catholics believe the visible head of the Church on earth is the bishop of Rome, the apostolic successor of Peter. But if the majority of historians say there was not one bishop of Rome for a century and a half, then there was not one apostolic successor to succeed Peter for quite some time. Long past the time when Catholics believe Jesus built His church upon Peter.
And then it was not even until the 3rd century until Peter’s apostolic successors declared their authority as Peter’s apostolic successors. Even further past Christ’s time on earth.
Apostolic Succession
Roman claim
The principle underlying the Roman claim is contained in the idea of succession…
Now the Roman Pontiffs come immediately after, occupy the position, and perform the functions of St. Peter; they are, therefore, his successors.
Beginning with the middle of the second century, there exists a universal consensus as to Peter’s martyrdom in Rome.
In the third century the popes claim authority from the fact that they are St. Peter’s successors.
newadvent.org/cathen/01641a.htm