But read all of Matthew 16. Read it in context. The disciples were confused about Jesus, both his teaching and his identity.
Then Peter correctly states who Jesus is, revealed to him by the Holy Spirit. This confession is what Jesus is talking about, and that Peter was the example of what to believe.
It is Christ who is the Foundation, the Rock, and Peter was identifying himself with that Rock, to which Jesus responded with great approval. It is like people naming their child “Grace” or “Faith.” The person is not faith or grace, but (it is the parents’ hope) that they will embody and be expressions of Grace or Faith, or Hope. In Peter’s pre-ressurrection days, he was anything but a rock, he was
The term ekklesia (church) in that day meant nothing more than “assembly” or “gathering.” There were words for Temples and Priesthoods and structures, but those terms were not used.
Also note that this is one single reference is scripture, nowhere repeated, and it is found in the Gospel that was written by a Jew, addressed to the Jewish community. Establishing the identity of Messiah was especially crucial in this community, that’s why it’s in Matthew.
As to the “keys,” this refers to the church universal, catholic, small “c.” God answers prayer. We have all (hopefully) seen “loosing and binding” that seems to have been tied to our prayers to Our Blessed and Wonderful Lord, though it is His action, not ours.
Mt.16.19 I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.”
Christ addressed Peter alone. The three words "you" in this passage are all singular. Christ was not speaking of prayers by members of the "universal, catholic, small 'c'" Church. He was speaking specifically to Peter and gave him "keys" for a single purpose. I explained what those "keys" were for in post #169.