Edit: Do you have an sources that would elude to the Early Bishops believing that they were all the successors of Peter? Hope that’s not snarky
I don’t have an article to link to but here’s some quotes…
Cyprian of carthage
“The Lord speaks to Peter, saying, ‘I say unto thee, that thou art Peter; and upon this rock I will build my Church, and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven; and whatsoever thou shalt bind on earth shall be bound also in heaven, and whatsoever thou shalt loose on earth shall be loosed in heaven.’ And again to the same He says, after His resurrection, ‘Feed my sheep.’ And although to all the apostles, after His resurrection, He gives an equal power, and says, ‘As the Father hath sent me, even so send I you: Receive ye the Holy Ghost: Whose soever sins ye remit, they shall be remitted unto him; and whose soever sins ye retain, they shall be retained;’ yet, that He might set forth unity, He arranged by His authority the origin of that unity, as beginning from one.
Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity.” (On the Unity of the Church, 4)
“Our Lord, whose precepts and admonitions we ought to observe, describing the honour of a bishop and the order of His Church, speaks in the Gospel, and says to Peter: ‘I say unto thee, That thou art Peter, and upon this rock will I build my Church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shall loose on earth shall be loosed in heaven.’ Thence, through the changes of times and successions, the ordering of bishops and the plan of the Church flow onwards;
so that the Church is founded upon the bishops, and every act of the Church is controlled by these same rulers.” (Epistle 26:1)