I don't know how covenant theology interpret this, but here are my thoughts. These covenants are one in the same - just different aspects or promises within the same covenant.
[Gal 3:6-18 NASB] 6 Even so Abraham BELIEVED GOD, AND IT WAS RECKONED TO HIM AS RIGHTEOUSNESS ((Covenant from Genesis 15)). 7 Therefore, be sure that it is those who are of faith who are sons of Abraham ((covenant from chapter 17)). 8 The Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, [saying,] "ALL THE NATIONS WILL BE BLESSED IN YOU." ((Covenant from chapter 12)) 9 So then those who are of faith are blessed with Abraham, the believer. -- 14 in order that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we would receive the promise of the Spirit through faith. 15 Brethren, I speak in terms of human relations: even though it is [only] a man's covenant, yet when it has been ratified ((covenant from chapter 15)), no one sets it aside or adds conditions to it. 16 Now the promises were spoken to Abraham and to his seed ((covenant Gen 9:9, 12:7, 13:16, 15:5,18, 17:7-10,12,19 etc etc) . He does not say, "And to seeds," as [referring] to many, but [rather] to one, "And to your seed," that is, Christ. 17 What I am saying is this: the Law, which came four hundred and thirty years later, does not invalidate a covenant previously ratified by God, so as to nullify the promise. 18 For if the inheritance is based on law, it is no longer based on a promise; but God has granted it to Abraham by means of a promise.
A promise (another word for promise is covenant)-- the whole covenant from these multiple chapters is one big promise.
[Rom 4:8-13 NASB] 8 "BLESSED IS THE MAN WHOSE SIN THE LORD WILL NOT TAKE INTO ACCOUNT." 9 Is this blessing then on the circumcised, or on the uncircumcised also? For we say, "FAITH WAS CREDITED TO ABRAHAM AS RIGHTEOUSNESS." 10 How then was it credited? While he was circumcised, or uncircumcised? Not while circumcised, but while uncircumcised; 11 and he received the sign of circumcision, a seal of the righteousness of the faith which he had while uncircumcised, so that he might be the father of all who believe without being circumcised, that righteousness might be credited to them, 12 and the father of circumcision to those who not only are of the circumcision, but who also follow in the steps of the faith of our father Abraham which he had while uncircumcised. 13 For the promise to Abraham or to his descendants that he would be heir of the world was not through the Law, but through the righteousness of faith.
[Gen 17:4-7 NASB] 4 "As for Me, behold, My covenant is with you, And you will be the father of a multitude of nations. 5 "No longer shall your name be called Abram, But your name shall be Abraham; For I have made you the father of a multitude of nations. 6 "I will make you exceedingly fruitful, and I will make nations of you, and kings will come forth from you. 7 "I will establish My covenant between Me and you and your descendants (seed, singular) after you throughout their generations for an everlasting covenant, to be God to you and to your descendants (seed, singular) after you.
Abraham was made righteous for his faith in the gospel of Jesus Christ. He is the "father of all who believe." He is the "father of many nations." (not just the nation of Israel) He believed God when God told him about Jesus Christ in Genesis 15:5-6, and for this faith in the gospel (Gal 3:8) he was made righteous. God says he will be the "father of many nations" and then immediately promises that the covenant will be established by those offspring from the many nations (not just the one nation of Israel).
This is the same covenant of Genesis 12, 15, 17. It is the covenant of faith.
[Gal 4:22-31 NASB] 22 For it is written that Abraham had two sons, one by the bondwoman and one by the free woman. 23 But the son by the bondwoman was born according to the flesh, and the son by the free woman through the promise. 24 This is allegorically speaking, for these [women] are two covenants: one [proceeding] from Mount Sinai bearing children who are to be slaves; she is Hagar. 25 Now this Hagar is Mount Sinai in Arabia and corresponds to the present Jerusalem, for she is in slavery with her children. 26 But the Jerusalem above is free; she is our mother. 27 For it is written, "REJOICE, BARREN WOMAN WHO DOES NOT BEAR; BREAK FORTH AND SHOUT, YOU WHO ARE NOT IN LABOR; FOR MORE NUMEROUS ARE THE CHILDREN OF THE DESOLATE THAN OF THE ONE WHO HAS A HUSBAND." 28 And you brethren, like Isaac, are children of promise. 29 But as at that time he who was born according to the flesh persecuted him [who was born] according to the Spirit, so it is now also. 30 But what does the Scripture say? "CAST OUT THE BONDWOMAN AND HER SON, FOR THE SON OF THE BONDWOMAN SHALL NOT BE AN HEIR WITH THE SON OF THE FREE WOMAN." 31 So then, brethren, we are not children of a bondwoman, but of the free woman.
[Isa 54:1 NASB] 1 "Shout for joy, O barren one, you who have borne no [child;] Break forth into joyful shouting and cry aloud, you who have not travailed; For the sons of the desolate one [will be] more numerous Than the sons of the married woman," says the LORD.
The children born from the desolate woman (the adopted children of the woman who didn't give birth to physical heirs) will be more numerous than the physical descendants of the promise of the covenant of faith.
The covenant of faith -- salvation through faith in the gospel of Jesus Christ -- first made Abraham righteous. Abraham was the first person made righteous through his faith in the gospel of Jesus Christ. He was the first man saved by grace through faith in the gospel. All who are his spiritual descendants -- those with the same faith in the gospel of Christ that Abraham had -- are inheritors of the covenant of faith... inheritors of the righteousness given to Abraham.
With the exception of Abraham, none of us are given righteousness directly for our faith. We all obtain our righteousness by our faith qualifying us as heir's of Abraham and then INHERITING the righteousness given to Abraham. This is why God calls it an Everlasting Covenant in Genesis 17:7 - assured to all the descendants of Abraham.