The Church in Mt 16 is defined as the Church that Christ builds, in some sense, on the person of St. Peter, to whom the Father reveals the divine sonship of Christ. It is then a church that is orthodox in doctrine and in communion with the Pope.
The Church is said to prevail against Hell, that is bring people to salvation.
Christ is the head of the church, His body. He is the stone the builders rejected that the church is built on.
There is nothing in any of Peter's writings which even refer to his alleged position of being pope, the head of the church. He made no recorded singular major correct decisions as an apostle. He leaves no written instructions on how his successor is to be identified much less chosen.
Catholics claim that Peter was the first pope, but there's a huge gap in time about 300 years, IIRC, between Peter and the recorded beginning of the institution we know of as the Catholic church. And there's not even the kind of unity within that that Catholic claim.
The unity of believers is the unity through the Holy Spirit, not the unity of church membership.