I don’t see any ancient explanations in here connecting the key of David in Isaiah 22:22 and Revelation 3:7 to the keyS in Matthew 16:19. I think that is a modern day idea. Or maybe you can prove me wrong.
I read your links. I am always skeptical when I see a list of brief quotes with “…” in them. I see a lot of people identifying Peter as rock. Of course as we have seen earlier in the thread, Tertullian stated the church was built on Peter, but denied the fact that there was any succession. I would wonder if we could read the whole chapter of each of the books quoted if they would confirm that the papacy was initiated when the church was built on Peter himself. (How many foundations can you build in one building?)
This quote is in your second link:
J.N.D. Kelly, one of the greatest patristic scholars of the 20th century, and an Anglican, writes to the contrary in his classic work Early Christian Doctrines (HarperSanFrancisco, 1978) :
“According to him [St. Augustine], the Church is the realm of Christ, His mystical body and His bride, the mother of Christians [Ep 34:3; Serm 22:9]. There is no salvation apart from it; schismatics can have the faith and sacraments…but cannot put them to a profitable use since the Holy Spirit is only bestowed in the Church [De bapt 4:24; 7:87; Serm ad Caes 6]…It goes without saying that Augustine identifies the Church with the universal Catholic Church of his day, with its hierarchy and sacraments, and with its centre at Rome…By the middle of the fifth century the Roman church had established, de jure as well as de facto, a position of primacy in the West, and the papal claims to supremacy over all bishops of Christendom had been formulated in precise terms…The student tracing the history of the times, particularly of the Arian, Donatist, Pelagian and Christological controversies, cannot fail to be impressed by the skill and persistence with which the Holy See [of Rome] was continually advancing and consolidating its claims. Since its occupant was accepted as the successor of St. Peter, and prince of the apostles, it was easy to draw the inference that the unique authority which Rome in fact enjoyed, and which the popes saw concentrated in their persons and their office, was no more than the fulfilment of the divine plan.” (Kelly, page 412, 413, 417)
Here is the link to the actual book for this one:
archive.org/stream/pdfy-CY7YNVnvFwggDjnT/103911481-J-N-D-Kelly-Early-Christian-Doctrines#page/n423/mode/2up
I do think that reading the whole chapter paints a different hue then is depicted in the selected phrases pulled out. Page 417 where the last quote is taken from begins a section where JND Kelly explains the formation of the papacy in approximately the 5th century.