Yes, the canon was set by Tradition (please see
CCC 120:
It was by the apostolic Tradition that the Church discerned which writings are to be included in the list of the sacred books.90 This complete list is called the canon of Scripture. It includes 46 books for the Old Testament (45 if we count Jeremiah and Lamentations as one) and 27 for the New.91
The Old Testament: Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua, Judges, Ruth, 1 and 2 Samuel, 1 and 2 Kings, 1 and 2 Chronicles, Ezra and Nehemiah, Tobit, Judith, Esther, 1 and 2 Maccabees, Job, Psalms, Proverbs, Ecclesiastes, the Song of Songs, the Wisdom of Solomon, Sirach (Ecclesiasticus), Isaiah, Jeremiah, Lamentations, Baruch, Ezekiel, Daniel, Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zachariah and Malachi.
The New Testament: the Gospels according to Matthew, Mark, Luke and John, the Acts of the Apostles, the Letters of St. Paul to the Romans, 1 and 2 Corinthians, Galatians, Ephesians, Philippians, Colossians, 1 and 2 Thessalonians, 1 and 2 Timothy, Titus, Philemon, the Letter to the Hebrews, the Letters of James, 1 and 2 Peter, 1, 2 and 3 John, and Jude, and Revelation (the Apocalypse).)
We agree Scripture was Scripture from the time quill met parchment/vellum/etc…
As Scripture (in the vast majority) doesn’t self-identify, the question is, how does one know what is Scripture?
You’ve referred to 2 Tim 3:16 (and surrounding verses) which point to a canon of the OT. I agree such canons existed.
The question then becomes: what was the canon to which Paul referred (as he doesn’t list it)?
Which raises the question you’ve not answered:
what was the canon in 2000 BC? in 1020 BC? in 200 BC? in 200 AD?
Was the canon automatically updated as soon as someone said, “I have produced another writing inspired by God”?