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."
“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.”
Wait, wait, Martha recited the formula too, so maybe she is a “rockette”!
John 11:27, “She saith unto him, Yea, Lord: I believe that thou art the Christ, the Son of God, which should come into the world.”