Paul was different, as he attests here. The apostles did not select him.
Which still leaves you with zero apostles appointed by Peter, while Acts 1 was by lots, by the community, not a papal appointee of even the candidates.
The title "Pope" only applied to the bishop of Rome.
But was not used of a single head till much later, and never in Scripture.
There was a Jewish cardinal of France who stood up to blessed John Paul II as well; Paul did not deny any apostolic doctrine, he addressed appearance and behavior.
Peter (whom you must mean) did indeed deny any apostolic doctrine, as what you do is what constitutes belief, (Ja. 2:18) and what Peter was believing at that time was inconsistent with what he confessed and had done.
Rome wants to be judged by what she says, but by their fruits ye shall know them.
Finally, the churches of Revelation are addressed separately. If there was "one" church, there would be only one church addressed. Sorry but there is nothing in scripture that supports your view.
Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints,..
This in no way refutes what was said. Even the epistle you quote from was an individual church, and while it was part of the "household of faith," it remains that the churches of Rev. are not addressed as one church.
The text you should have quoted is from Peter himself, "to the strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia." (1Pt. 1:1)
But which shows Peter exercising a general pastoral role, which is not to be denied. But in which he is simply called "an apostle," "an elder," "a servant," and for whom the "more suere word of prophecy" is Scripture. And nothing here or anywhere supports Peter being the first of a line of exalted infallible heads. What you need for that is at least references in the church epistles to look to and submit particularly to Peter, or churches, as in Rv. 2,3, being chastised for not submitting and this being set forth as a solution to their problems. And formulaic infallibility promised for for Peter and successors . But that is nowhere provided, or necessary.
Time for bed. If there was "one" church, there would be only one church addressed. Sorry but there is nothing in scripture that supports your view.
There certainly wasn’t a message addressed to the “church of Rome” in Revelation....(in support of your posting).
(and we do know there were Christians and functioning groups under persecution in Rome at the time of John....as denoted by John’s own banishment to Patmos)