Its Cathloic and here is why
You need to remember first of all that at the time St. Paul wrote this there was only one Church – the Catholic Church. There was no such thing as a Christian that was not Catholic. So when St. Paul refers to the Church he is referring to the Catholic Church – the only church in existence. When we talks about the believers he is talking about fellow Catholics – the only kind of Christian in existence at the time. And, that Church was headed by the successor to St. Peter. It was a fellowship of believers under the leadership of the Bishop of Rome.
Here, St. Paul says the the Church, under the leadership of the Pope, is the pillar and foundation of truth. The Bible is not that pillar and foundation, but the Church.
We must remember that the New Testament did not exist for decades after the Resurrection of Jesus. And even when the Apostles started to write down the letters that we now consider to be Scripture, the faithful were reading all sorts of documents in their Masses. The Bishops in the 4th Century had to decide which of these circulating manuscripts were really Scripture and which were not.
So it was not until the 4th Century that the faithful really knew what constituted the New Testament. It was Catholic Bishops who decided this. One of the tests they applied to these manuscripts was whether or not the manuscript taught the faith that match when the Church was already teaching orally.
Bottomline: the Church did not come from the Bible, the Bible came from the Church and was a written form of what the Church had been teaching orally for hundreds of years. In fact, the New Testament is a Catholic document of the faith. It was written by Catholics, vetted by Catholics, and declared inerrant and infallible Scripture by Catholics.
So why does the Catholic Church think that this verse refers to the Catholic Church? Because the Catholic Church was the only Church at the time, and Jesus established His Church upon Peter as Prime Minister and thus the only true Church in the fullness of the faith is that church, that group of people, who are loyal and obedient to the successor of St. Peter, the Bishop of Rome, the Pope. This was ordained by God personally and no one has a right to contradict God.