The Catholic Church teaches that Jesus is the petra and “Petros/Peter is the Christian people?” Simon was called Peter so “in a figure, that he should signify the Church?”
I don’t think anywhere in the quote from Augustine (or in any quote by him or anyone before him) did he say that this meant that Simon-Peter was a “physical counselor and guide” who had successors to his seat.
I won’t disagree that Simon-Peter was foundational in the church. Didn’t he get things going while filled with the Holy Spirit at Pentecost? He was of prime importance. A foundation is something that comes first and then everything else is built on it. A foundation doesn’t get replaced every generation. Each structure can have one foundation. Peter in many ways was the first to be built on the foundation of Christ. 1 Peter 2:5