It is only Gen 2:5-11:26 that is the later addition. This was inserted after the core of the "Pentateuch" or "Quadrateuch" had been completed. It seems that whoever wrote Deuteronomy is likely the same person who wrote the second creation account in Genesis.
So, why this proposal? If you look at how the rest of the Deuteronomistic material references Genesis, it is quite clear that Gen 2:5-11:26 is glaringly absent. Yet, there are references to material from the first creation account.
For example:
Genesis 2:1 Thus the heavens and the earth were finished and all their multitude. 2 On the sixth day God finished the work that he had done, and he rested on the seventh day from all the work that he had done. 3 So God blessed the seventh day and hallowed it, because on it God rested from all the work that he had done in creation.
This is the basis for the Sabbath, which is discussed at length throughout the Pentateuch, for example in the giving of the 10 Commandments:
Exodus 20:8 “Remember the Sabbath day and keep it holy. 9 Six days you shall labor and do all your work. 10 But the seventh day is a Sabbath to the Lord your God; you shall not do any work—you, your son or your daughter, your male or female slave, your livestock, or the alien resident in your towns. 11 For in six days the Lord made heaven and earth, the sea, and all that is in them, but rested the seventh day; therefore the Lord blessed the Sabbath day and consecrated it.
Likewise, when we read Genesis 11, there is a mention of the flood following the story of Babel:
Genesis 11:10 These are the descendants of Shem. When Shem was one hundred years old, he became the father of Arpachshad two years after the flood, 11 and Shem lived after the birth of Arpachshad five hundred years and had other sons and daughters.
But we also don't find any references to the figures listed from Gen 11:10-Gen 11:27 elsewhere in the Pentateuch, yet we do find references to Abram, Nahor, and Haran in other Deuteronomistic material. These figures are mentioned in Gen 11:27:
27 Now these are the descendants of Terah. Terah was the father of Abram, Nahor, and Haran, and Haran was the father of Lot. 28 Haran died before his father Terah in the land of his birth, in Ur of the Chaldeans. 29 Abram and Nahor took wives; the name of Abram’s wife was Sarai, and the name of Nahor’s wife was Milcah. She was the daughter of Haran the father of Milcah and Iscah. 30 Now Sarai was barren; she had no child.
So it seems to me, that originally, the work began with the first Creation account, which establishes the basis for the Sabbath. This then was followed by the introduction of Abraham and his family, which begins with Genesis 11:27. Perhaps something was modified when the second creation account was added, but generally, it went from Gen 2:4 to Gen 11:27. Maybe some wording was changed a little to connect Gen 26 to what is now Gen 27, who knows.
But you'll notice that Terah, Abram, Nahor, and Haran are featured throughout Genesis on into Genesis 20 and beyond, while figures from prior to Terah are not. So figures like Shem, Peleg, and Serug are only mentioned in Gen 11 an nowhere else.
But Deuteronomy pics up material from Gen 2:5-11:26 again in places. Also the general character of Deuteronomy is different than Gen 12-Numbers and it has a summary function. so it seems that Deuteronomy is a later addition by a different writer, who also knows material from Gen 2:5-Gen 11:26.