Catching up with this thread across time-zones, so replies may end up duplicating others.
In terms of covenants, that with Abraham is God’s first announcement of a global salvation project. Noah simply preserves (sinful) life from de-creation, doing nothing to extend God’s glory, though achieving stability.
But the elements in the promise to Abraham echo those of the beginning (land, people, blessing). He is promised that he will achieve what Adam failed to do, and narratively his call marks the break from the “Old Testament of the Old Testament”, Gen 1-11. It is a “new thing”.
Next, this covenant with Abraham is expressly applied to Jesus by Paul, and also is used in Deuteronomy as the basis for that new covenant which will replace Moses’ own covenant, in the event of its inevitable failure.
So, turning to the time of Moses, we can see the call of Israel (by the Mosaic covenant) as the first culmination of the promise to Abraham, intended to bring blessing to the world and glory to God, but failing through unbelief, even as it begins.
But we can see the ministry of Jesus (by a new covenant, announced explicitly at the time of Israel’s exile) as being the successful fulfilment of the same Abrahamic promise in a new form.
Meanwhile, back at the ranch, Israel’s story (rather than Abraham’s) closely mirrors that of Adam of call, presence, failure through disobedience, ending, as we know, in exile. “Adam is Israel”, for better and worse.
And so the key salvific figures are Adam (), Israel as a nation (Adam redividus ), and Jesus, who is both the new/last Adam and the true Israel .
The other covenant figures fit into that big scheme both historically and typologically: Noah’s covenant forms the stable world in which God’s long-game is played, and as a saviour-figure, including water, may be legitimately be compared to Christ.
Abraham’s covenant is the “master-plan” of salvation by grace through faith, and as exemplifying these Abraham is typologically the father of all believers, as well as the ancestor of both Israel and Jesus. But his own role in history is limited to being an initiator - he is not the new Adam, and neither are the individual patriarchs.
Israel the nation, as I have said, has the potential to remedy Adam’s failed mission to the world, but they break their covenant through unbelief. But still, they are represented as doing Adam’s work.
David’s covenant is, historically, a way to retrieve Israel’s mission, as the righteous king who restores his people to God. But prophetically and typologically, it primarily foretells Jesus as being a royal figure achieving that same role for all mankind. David’s personal mission is only to Israel - he is not a new Adam.
Opinions vary as to whether Adam’s own mission is covenantal - I would argue that it is, though for obvious historical reasons it lacks the “2nd millennium ANE covenant format”.
And lastly, the “eternal covenant” which the Reformers saw between the Father and the Son is the overarching plan encompassing all the other covenants, and all history. Conveniently that makes for a total of 7 biblical covenants, 3 of which (Adam, Moses, Jesus) are clear episodes in the salvation history, and/or (in the simplest arrangement) 2 of which represent the Fall (Adam) and God’s remedy (Abraham).