We can see more of what Cyprian understands of unity (in a writing that actually mentions the rock and the keys) coming from one source in his Treatise,
On the Unity of the Church.
“4. If any one consider and examine these things, there is no need for lengthened discussion and arguments. There is easy proof for faith in a short summary of the truth. The Lord speaks to Peter, saying, I say unto you, that you are Peter; and upon this rock I will build my Church, and the gates of hell shall not prevail against it. And I will give unto you the keys of the kingdom of heaven; and whatsoever you shall bind on earth shall be bound also in heaven, and whatsoever you shall loose on earth shall be loosed in heaven. And again to the same He says, after His resurrection, Feed my sheep.
And although to all the apostles, after His resurrection, He gives an equal power, and says, As the Father has sent me, even so send I you: Receive the Holy Ghost: Whose soever sins you remit, they shall be remitted unto him; and whose soever sins you retain, they shall be retained; John 20:21 yet, that He might set forth unity, He arranged by His authority the origin of that unity, as beginning from one.
Assuredly the rest of the apostles were also the same as was Peter, endowed with a like partnership both of honour and power; but the beginning proceeds from unity. Which one Church, also, the Holy Spirit in the Song of Songs designated in the person of our Lord, and says, My dove, my spotless one, is but one. She is the only one of her mother, elect of her that bare her. Song of Songs 6:9 Does he who does not hold this unity of the Church think that he holds the faith? Does he who strives against and resists the Church trust that he is in the Church, when moreover the blessed Apostle Paul teaches the same thing, and sets forth the sacrament of unity, saying, There is one body and one spirit, one hope of your calling, one Lord, one faith, one baptism, one God? Ephesians 4:4”
newadvent.org/fathers/050701.htm
So Cyprian does understand Rome to have a symbolic unity, but an equal authority. This is best noted in his disagreements with Bishop of Rome Stephen who Cyprian disagreed with regarding re-baptism of heretics. Cyprian and 87 Bishops gathered to oppose Stephen and all agreed that:
“**For neither does any of us set himself up as a bishop of bishops, nor by tyrannical terror does any compel his colleague to the necessity of obedience; since every bishop, according to the allowance of his liberty and power, has his own proper right of judgment, and can no more be judged by another than he himself can judge another. But let us all wait for the judgment of our Lord Jesus Christ, who is the only one that has the power both of preferring us in the government of His Church, and of judging us in our conduct there.”
**
newadvent.org/fathers/0508.htm
I have not heard of Optatus before. This is the first thing that I read from him. I see that he is writing against the Donatist heretics who had separated from the church. I don’t see anything that would make me think that he is doing anything more that echoing Cyprian in symbolizing unity in the cathedra of Peter.