Isn't Matthew 16:19 pretty clear in the matter that Jesus is assigning the power of binding and loosing to Peter, i.e. including the appointment of successors as the Rock of the Church?
I think your catechism gives a good explanation of whom the Rock is:
424 Moved by the grace of the Holy Spirit and drawn by the Father, we believe in Jesus and confess: 'You are the Christ, the Son of the living God. On the rock of this faith confessed by St. Peter, Christ built his Church.
The Rock is Jesus and the church is built on our Faith in Jesus the Christ, the son of the living God. The church militant is the body of indwelt believers.
Luke 17:20-21 Now when He was asked by the Pharisees when the kingdom of God would come, he answered them and said, "The kingdom of God does not come with observation, nor will they say 'See Here!' or 'See There!' For indeed, the kingdom of God is within you."
Then why was it that James the Just, blood brother of Jesus, was the first ruling Apostle in Jerusalem after the crucification - with John and Peter basically in councilor positions, these three making up what Paul sneeringly referred to as "The so-called pillars of the Church"
It's all in the NT - James was the head Apostle until his death - stoned in the courtyard of the Temple by Temple Priests, in 62AD - and then other family members of Jesus succeeded - it's all there in the New Testament - the book that the Roman Church that came into being some 300+ years after the crucification, forbade, on pain of torture/death, to own or read for themselves - that they kept from being translated into the peoples own languages so they COULD - (Blast that Luther and King James!) = my own ancestors were arrested, harried and driven to sell their homes and, ultimately, leave their countries in order to have the freedom to own/read the Bible...and follow what Jesus, Himself, actually taught -