It is on Peter himself, the confessor of his Messiahship, that Jesus will build the Church. Attempts to interpret the 'rock' as something other than Peter in person (e.g. his faith, Jesus, etc.) are due to Protestant bias, and introduce to the statement a degree of which is highly unlikely
*Have a good night's sleep,brother
As a Magisterial Presbyterian -- the Heir of the Scottish Church founded by Greek Missionaries from Asia Minor long before the Roman-Papist Usurpation -- I do not doubt, deny, nor dispute the Scriptural Fact that Jesus Christ did Himself Personally-ordain the Apostle Saint Peter to play an absolutely-foundational role in the establishment of the New Testament Church amongst the Jews, just as Our Lord also Personally-ordained the Apostle Saint Paul to play an absolutely-foundational role in the establishment of the New Testament Church amongst the Gentiles (Galatians 2:8).
All of which does nothing to change the fact that, according to Acts 15, the God-Ordained Organization of the New Testament Church IS CONCILIAR, AND NOT PAPAL; and that it was Apostle James the Brother of Jesus, AND NOT PETER, who pronounced the Judgment of the Council.
When all is said and done, you can't argue with Acts 15.
The Government of the Church is Conciliar, NOT PAPAL; and James was the first "President", NOT PETER.
Best, OP