Not disputing the quote from Irenius above, It is also possible to interpret the numbers of Divine covenants as being greater in number:
The covenant with Adam giving him the Garden of Eden. That was replaced in the expulsion with the granting him and his descendants with stewardship over the Earth, and the commandment to “Go Forth and Multiply”
Then came the covenant with Noah: God will never again destroy the whole Earth with a flood.
Then came the covenant with Abraham, and granted to his descendants.
The Covenants of Moses (x2) followed at the time of the Exodus and shortly after. These start with the Passover and are developed into the law of Moses.
The Covenant of David then follows, defining a Kingship.
The Words “Testament” and “Covenant” are fluid in a scriptural and theological sense. they mean the same thing.
The covenants of the Old Testament were Archetypal and Didactic/Pedagogical
They served in the first instance to inform Man that God was there and wanted a relationship.
Then they served to draw Gods Chosen People closer to Him, to guide them to the point in time when they would Receive the Incarnation, and thereby pass the New Covenant to the whole World. Everything in the Old Covenants served as an archetype that pre-figured and pointed to the structure of the New Covenant.
The New Covenant defined by Jesus, and stewarded by His Holy Church is the fulfilment of the Old Covenants. It’s Law is not written on tablets of stone, but written in our Hearts. (The Church calls this “Natural Law”)
It’s priesthood is no longer inherited from Aaron and Moses, sacrificing burnt offerings of animals, but has it’s High priest in “The Order of Melkisidek” who is High Priest and King, and who offers a Sacrifice of Bread and Wine.
The Sin Offering of the Mosaic Covenant is Pre-figured in the archetypical sacrifice of the Passover Lamb - and finds it’s fulfillment in the sacrifice of the Lamb of God on the Cross of Calvary.
This is Re-Presented to us by our Priests at Mass. that same sacrafice made present again, in the form of Bread and Wine - The Last Supper, and the Cross of Calvary made present on every altar at every Mass. We eat of the flesh and drink of the blood of that same Sacrificial Lamb in the form of (what looks like but no-longer is) Bread and Wine.
We see the Archrtype of this miracle in the Mana from Heaven. Bread coming from God via Moses. we now have the Bread that comes from Heaven that is Jesus, by the hands of the new priesthood.
The Redemption of the every Firstborn of Israel was made by the granting to the Aaronite Priesthood the tribe of Aaron, and all others had to be redeemed by a Redemption sacrifice.
We have been redeemed by the Sacrafice of Christ on the Cross. the Firstborn of God Himself: The Firstborn of All Creation.
The Arc of the Covenant is replaced with a Living Arc, and She who bore the new covenant within her womb, has been crowned Queen of Heaven.
Just as David took and took Him to the Hill country of Judea, so Mary went to visit her Cousin Elisabeth in the same place. Just as David danced before the Arc, so John danced before the Arc of the New Covenant, while within his own mothers womb.
The Archetypes, the paralells, The Pre-figuring of all the doctrine and traditions of our Holy Church come from the Old Covenant(s) and the Old Testament.