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"These books the church holds to be sacred and canonical not because she subsequently approved them by her authority after they had been composed by unaided human skill, nor simply because they contain revelation without error, but because, being written under the inspiration of the holy Spirit, they have God as their author, and were as such committed to the church". - First Vatican Council. (emphasis added by me for clarity)."

You should have emphasized the rest of that phrase as well, "after they had been composed by unaided human skill,". Then the sentence makes sense. The Church would never have approved, "by her authority", books which were not written under the inspiration of the Holy Spirit and call them sacred. That's the grammatical sense of the sentence, my friend.

The books were authored by God, of course, and were committed by Him to His Church. The bishops of that Church selected the correct, inspired books from the many different "gospels" and "epistles" which were floating around during the three centuries after Christ. You should see how many apocryphal books were extant. It was a large number.

By the way, we wouldn't even have the New Testament if the Church had not compiled the various books and determined that they, and they alone, were the inspired canon of Scripture.

Because your argument was that we have the New Testament because the Church compiled the various books and determined that they, and they alone, were the inspired canon Scripture. You did not state HOW they did this, just that they did it.