Mostly pertains to the use of the Septuagint vs the Hebrew Bible. For the formation of the New Testament, see Canonization of the New Testament.
Why did the canon vary in the early church?
The church fathers outside of Palestine and Syria used the Septuagint, but they recognized a wide canon of esteemed books (including the Apocrypha) and a narrow canon of the inspired books of the Hebrew Bible. The Apocrypha were known in the church from the start, but the further back you go, the more rarely they are considered inspired.
Within the Bible itself, the Apocrypha are not validated by Jesus nor New Testament writers, except for two apparent references in Jude. The Assumption of Moses is said to be referenced in Jude 1:9 (Origen mentioned the book was extant in his time and contained this account between Michael and the devil and he supposed this is the source of this verse, but the book is lost to time. (https://www.gotquestions.org/Michael-Satan-Moses.html)) and Enoch in Jude 1:14. Of course, references do not mark the source as divinely inspired, though, as the bibliography of the Bible shows, all kinds of history, poetry, and drama is referenced.
What evidently happened in the early centuries of Christianity was this (or so Beckwith says): Christ passed on to His followers, as Holy Scriptures, the Bible He had received, containing the same books as the Hebrew Bible. The first Christians shared a full knowledge of the canon with their Jewish contemporaries. However, the Bible was not yet one book, rather it was a memorized list of scrolls. The breach with Jewish oral tradition, the alienation between Jew and Christian, and the general ignorance of Semitic languages in the church outside of Palestine and Syria led to increasing doubt concerning the canon among Christians, which was accentuated by the drawing up of new lists of the biblical books arranged on other principles, and the introduction of new lectionaries.
Such doubt about the canon could only be resolved in the way it was resolved at the Reformation--by returning to the teaching of the New Testament and the Jewish background against which it is to be understood.
(The Origin of the Bible: Newly Updated by F. F. Bruce, J. I. Packer, Philip W. Comfort, and Carl F. H. Henry, 2020. The Canon of the Old Testament by R. T. Beckwith. Pages 62-64, 74.)
In A.D. 367, Bishop Athanasius of Alexandria set out to dispel all confusion about the Old Testament canon in his Festal Letter 39. He included Baruch and the Epistle of Jeremiah and excluded Esther.
Festal Letter 39 by Bishop Athanasius of Alexandria, point 4; New Advent, LLC - From Letter 39 @ https://www.newadvent.org/fathers/2806039.htm, accessed June 6, 2023.)
At the Third Council of Carthage, they declared the canon. They included five books of Solomon, Tobit, Judith, two books of Esdras, and two books of the Maccabees.
(A General Survey of the History of the Canon of the New Testament: Fourth Edition, with New Preface, by Brooke Foss Westcott, D.D., Regius Professor of Divinity, and Late Fellow of Trinity College, Cambridge, 1875, Pages 435-436, @ https://archive.org/details/ageneralsurveyof00westuoft/page/388/mode/2up?q=%22carthage%22)