The question has a lot to unpack:
Assumption: Paul seems to never appeal to covenant to authenticate his gospel and justification by faith alone
I disagree strongly, as Paul makes repeated references to the covenant with Abraham to support justification by faith in Romans. In fact, the Abrahamic covenant is the whole basis of Paul's argument. Unless by "covenant", you are excluding Abraham's covenant and focusing only on Jeremiah's prophecy.
But deciding the details of covenants from prophecy is a tricky business. Is this covenant prophecied by Jeremeiah truly not mentioned in any other prophet that Paul may have cited? Not in Isaiah, not in Ezekiel? But God only revealed it to Jeremiah?
For example, we have in Jer 32.37:
Behold, I will gather them out of all countries, whither I have driven
them in mine anger, and in my fury, and in great wrath; and I will
bring them again unto this place, and I will cause them to dwell
safely: And they shall be my people, and I will be their God: And I
will give them one heart, and one way, that they may fear me for ever,
for the good of them, and of their children after them: And I will
make an everlasting covenant with them, that I will not turn away from
them, to do them good; but I will put my fear in their hearts, that
they shall not depart from me.
Which appears to be the same covenant as in Ezekiel 37.26-27:
I will make a covenant of peace with them. It shall be an everlasting
covenant with them. And I will set them in their land and multiply
them, and will set my sanctuary in their midst forevermore. My
dwelling place shall be with them, and I will be their God, and they
shall be my people.
And also in Zecharaiah 2.10-11
Sing and rejoice, O daughter of Zion, for behold, I come and I will
dwell in your midst, declares the Lord. And many nations shall join
themselves to the Lord in that day, and shall be my people. And I will
dwell in your midst, and you shall know that the Lord of hosts has
sent me to you.
Which certainly seems to support Paul's "grafted in" theory in which the gentiles would be included in the covenant.
But there's more, that covenant together with the grafted in theme also looks like it makes an apperance in Hosea 2.23-3.1:
And it shall come to pass in that day, I will hear, saith the LORD, I
will hear the heavens, And they shall hear the earth; And the earth
shall hear the corn, and the wine, and the oil; And they shall hear
Jezreel. And I will sow her unto me in the earth; And I will have
mercy upon her that had not obtained mercy; And I will say to them
which were not my people, Thou art my people; And they shall say, Thou
art my God. Then said the LORD unto me, Go yet, love a woman beloved
of her friend, yet an adulteress, according to the love of the LORD
toward the children of Israel, who look to other gods, and love
flagons of wine.
Which was directly cited by Paul in Romans 9.25.
But that looks a lot like Isaiah's promise of a new covenant in Is 59.21:
“And as for me, this is my covenant with them,” says the Lord: “My
Spirit that is upon you, and my words that I have put in your mouth,
shall not depart out of your mouth, or out of the mouth of your
offspring, or out of the mouth of your children's offspring,” says the
Lord, “from this time forth and forevermore.”
And the above passages are certainly cited by Paul in several other places.
But let's see if we can find references directly to the original passage in Jeremiah in Paul's writings:
2 Cor 3.3:
Forasmuch as ye are manifestly declared to be the epistle of Christ
ministered by us, written not with ink, but with the Spirit of the
living God; not in tables of stone, but in fleshy tables of the heart.
2 Cor 6.16:
And what agreement does the temple of God have with idols? For we are
the temple of the living God, just as God said, “I will live in them
and will walk about among them, and I will be their God and they will
be my people.”
Wherefore come out from among them, and be ye separate, saith the
Lord, and touch not the unclean thing; and I will receive you, And
will be a Father unto you, and ye shall be my sons and daughters,
saith the Lord Almighty.
And there is, of course, the biggie, namely the last supper, e.g. in Matt 26.28
for this is my blood of the covenant which is poured out for many for
the forgiveness of sins.
Now did Paul know about the "new covenant" declared by Christ and associate it with Jeremiah's/Hosea's/Ezekiel's/Isaiah's/Zecharaiah's promised new covenant? Yes, I think the last supper was foundational theology for the new church.
Anyways, I could go on, but if there is one thing I've learned when reading prophecy, it's that absolutely nothing of substance appears in only a single prophet. The same things are repeated all over, but with some different emphasis and presentation. There are not 7 new covenants promised, there is only a single new covenant, brought on by the Messiah.
one body and one Spirit
(just as also you were called with one hope of
one God and Father of
all, who is over all, and through all, and in all.
Eph 4.4-6 LEB
They are merely revealed with slighly different presentations in the various prophets and then realized on earth during the last supper and then described gloriously by John in Revelation.