That Peter was the first Pope? Well, no. The word “Pope” does not appear in the Bible. “The rock” in every other instance has a specific meaning that does not refer to either the Pope, Peter or the Catholic Church. You’ve been provided a cite from one of your own early church fathers, contradicting the claim that Peter was the first Pope.
It would be very helpful to your case for there to be some authoritative, period documentation or early reference that validates the claim. Thus far you’ve provided none.
I’d suspect, myself, that the Apostles and early Christians as a whole would be horrified at the suggestion that a man given the Roman imperial title, “Pontifex Maximus,” a title borne by Nero, Caesar and Caligula, would ever become the titular head of all their different churches.
That is your interpretation.
The word POPE comes from the latin “Papa” which means Father and/or Spiritual Leader.
You are confusing everything that you think should or should not be noted in the Bible, with “language”
Not everything regarding various religious “sectarian” belief, doctrine, or traditions will be found in the Bible.
In your Bible in the Book of Acts, who was it that addressed the First Council, the Council of Jerusalem?
Peter of course, for he was the leader, the Pope, although that exact word is not used.
Don’t get hung up on little details when it’s right there in the Bible for you to read as Peter addresses the Council of Jerusalem.