The following is basically what I have received over the last couple of years in a fairly liberal mainline protestant seminary.
The scholarship I am aware of divides out the Joseph narrative as coming from a northern (Ephraim) source assembled into Genesis after the Babylonian exile. You can see the typical P (priestly) source lineages in Genesis 36 acting as glue between the Jacob/Israel transformation narrative and the Joseph narrative.
The main difference between the Jacob and Joseph stories is that the conception of God is far more pro-active in the Joseph story and following the noble hero. This is compared to how Jacob tricks the birthright/blessing out of Isaac through flat out lies. Lies that even include the name of God (Genesis 27:20). This connects with the reactive nature of God in the J text of the Jacob story (which includes such reactivity as being sorry for creating humanity before the flood).
But the Joseph story involves a pro-active God who famously "uses for good what they intended for evil" (Genesis 50:20). It rewards Joseph as far more of a benevolent hero than a trickster leader like Jacob (who's name literally means "trickster").
You can see more of this as well in the fact that Benjamin is born last, after his father's struggle with god/man (Gen 32) and renaming to Israel. His mother names him "son of my sorrow" and then dies, but Jacob renames him "son of the right hand" (ben-jamin). This becomes a kind of polemic against Saul, the first king, who was usurped by David and portrayed unfavorably in order to shore up the Davidic monarchy against criticism. Saul was a Benjaminite. You can also see a similar polemic at the end of Judges when the Benjaminites are slaughtered for their evil deeds. But it is always more complicated than this. "The right hand" is a position of privilege next to the patriarch. The tribes respected one another even in their conflicts, it seemed.
So for time periods, this places the Jacob story (being written) sometime around the time of David. This is primarily thought because the narrative involves a bunch of labeling of neighbors as respected family, but not blessed or chosen (e.g. Lot, Esau, etc). This narrative labeling is a power play that may indicate that it was written from a position of power and privilege as opposed to the subversive poetry of Isaiah 40-55 written from slavery considering what went wrong. It is a power play to call the edomites (in Esau) hairy dopes, but older brothers who we tricked, and the moabites (in Lot) as inbred cousins (his daughters slept with their dad). There is only one time period where that kind of power play makes sense, the apex of power in David/Solomon.
The Joseph story is typically thought of as coming from from a contemporary source, but from the north, and attached to the narrative after the northern parts of Israel were conquered by the Assyrians (c721 BC). The northern israelites would have fled to Jerusalem and become subordinate to the Judeans.
But it is also thought that all of the torah was massaged together and tweaked after/during Babylonian exile in the 6th century BC. Hence the glue of chapter 36 that lays down details of the society to try to re-establish their identity after catastrophe. Those lineages are typically glue as can also be seen in Genesis 5 and other places.