It is ironic that the same councils Protestants point to as authoritative in settling the New Testament canon were also used by the Church to authoritatively settle the Old Testament canon.
However, historical or not, someone took out 7 books from what the Canon of the Bible had been decided by the Council of Carthage. This change does historically show up in Western Europe in the 15th century--at the time of the Reformers.
The OP is asking who gave them the authority--after at least 1100 years, to make those changes.
They did not have the authority, and they should not have done it. It was an error on the part of Luther and the Reformers.
Having made the error, and the error having been accepted, the shorter abridged Protestant Canon of 66 books has now become one of the most sacred traditions of Protestantism, and as Catholics we know how important Tradition is.
The change having been made, it now must be defended, because it is their Tradition.
We have to deal with the same thing: unwise decisions and bad acts of the historical Church that we then are called to somehow defend, because if we don't - if we admit to an error - then for many the whole edifice of religion comes crashing down.
For my part, I recognize that the Bible itself is simply not "all that". Jesus didn't teach from it. Neither did any of the Apostles. They referred to a passage here, a passage here, but there was no Bible until the 300s AD. So, in truth, the Bible really is not vitally important. What Christ SAID is what is important.
That comes down through tradition, and Jesus understood that the easiest way to convey that tradition over time is through a continuous institution: ergo the Church. The Church understood that the easiest way to keep track of tradition and teach itself and its clergy was to have the record in writing: ergo the Bible.
But the utility of a canon, and the Bible, easily lapses into idolatry and exaggerated claims of authority, just as the utility of an institution easily lapses into idolatry and exaggerated claims of authority about it.
How do we know the Christian Churches - all of the old ones, are rife with errors and exaggerations and mistakes? They all killed people. That is prima facie evidence of error and sin. We know from their deeds that they were not infallible, because they failed.
That doesn't mean that the books, the canons, what they have brought forward, is not good. It DOES mean most certainly that none of the traditions are perfect. They're all imperfect. Everybody - Protestant, Catholic, Orthodox engages in idolatry when they claim their book, their church, etc. is infallible. We know that's not true: they murdered people.
Because they are all in error, none of them has the towering authority they all claim.
Which doesn't mean we chuck 'em, but it DOES mean that we can see the tomfoolery when its before us.
Truth is, the different Eastern Churches have canons of different lengths, the Catholic Church has a canon of a certain length, the Protestants have a canon of a certain length, it's all tradition, and none of it matters. Truth is, the words of Jesus in the Gospels, Acts and Revelation - that's the marrow of all that writing, and they've all got that. The rest is additional information which is nice, but ancillary.
Nobody's ever going to admit to error, because they're all puffed up with the sin of pride, and they all defend the indefensible. Martin Luther had people burnt as witches. Calvin had an opponent burnt as a heretic. The Catholic Church killed a lot of people in that era. They were all crackpots and NONE of them had true divine authority - would God murder people for differences of opinion? No. So all of them were ruled by pride and the devil at that time, and nobody should be defending them too terribly hard.
When people do, it's because of the idolatry of tradition.
We really should all know better.
All of us.
WHY were all of them so filled with error and evil? Well, in large part because their solution to arguments they could not answer was to simply torture and murder their opponents, if they could. Therefore Pope Leo, and Martin Luther, and John Calvin, and John Knox all succeeded in carving out petty little religious dictatorships within the reach of their arms and prosecutors, and in the process made sure that ALL of their arguments are weak, stupid and indefensible in the face of ANY good lawyer from ANY side today.
Once you start murdering people over differences in religion, you're at the level of Muslim fanatics and you have by the very act of murder, absolutely ceased to speak with any credible authority about the real God.
Truth is, the Reformation Era is a black hole of Christian evil and stupidity, everybody was wrong, blood is all over the place, and all of the Biblical canons that came out of it are fine, because the Bible just ain't all that, and all of the canons have the Gospels, Acts and Revelation, which contain among them every single word that Jesus every said.
HE is God - the rest is just detail and you're better off chucking the lot of it rather than killing a single man over it.
You may now all carry on with your bickering. I've said my piece and am out of here.