Given that throughout the entirety of the Old and New Testament it was stated by God over and over again that He was the Rock “and there is no other” it is entirely in context that the Apostles would have understood that Jesus was speaking of Himself.
Peter indeed had just acknowledged that Jesus was the Christ the Son of the living God. Therefore acknowledged that Jesus was indeed the Rock referred to throughout scripture.
It would be out of context to believe that after declaring throughout scripture God is the rock to then believe by one statement He changed that.
If you want reference to God as the Rock here are some verses.
Deut. 32:4 He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.
2 Sam. 22:2 And he said, The LORD is my rock, and my fortress, and my deliverer; 3 The God of my rock; in him will I trust: he is my shield, and the horn of my salvation, my high tower, and my refuge, my saviour; thou savest me from violence.
Psalm 18:31, "And who is a rock, except our God."
Isaiah 44:8, "Is there any God besides Me, or is there any other Rock? I know of none."
Rom. 9:33, "Behold, I lay in Zion a stone of stumbling and a rock of offense, and he who believes in Him will not be disappointed."
1 Cor. 3:11, "For no man can lay a foundation other than the one which is laid, which is Jesus Christ,"
1 Cor. 10:4, "and all drank the same spiritual drink, for they were drinking from a spiritual rock (petras) which followed them; and the rock (petra) was Christ."
To believe that Christ is the Rock is totally in context and to believe otherwise is out of context.
It seems to me the problem with your interpretation is that Jesus does not say, “Your confession is rock, or I am Rock.”
He says quite clearly to Simon, “Thou art rock” and “Upon this rock, I will build my church.”
No way to get around that, no matter how you interpret it, what language you use or if it’s little or big, masculine or feminine.