What does the story of Yosef's separation and reunification hint to?

As is well known, "maaseh avot - siman lebanim" (the deeds of the forefathers are a sign for their descendants). Yoseph and Yehuda were the two leaders among the brothers. Later in our history, after the death of King Solomon, the Jewish people were divided into two states - Yehuda and Israel. The main leader of the northern state of Israel was the tribe of Yoseph, and the prophets often called the Northern Kingdom "Yoseph" or "Ephraim." In the end of days, the prophets promised that Yoseph and Judah would be reconciled again and become one kingdom, and so we read in the Haftorah of our Parsha (Ezekiel (37:16): “And you, son of man, take for yourself a staff and write on it: ‘For Yehudah and for the children of Israel who are united with him.’ And take another staff and write on it: ‘For Yoseph, the staff of Ephraim, and for all the children of Israel with him.’ And bring them one near the other, and they will become one in your hand… Behold, I will take the children of Israel from among the nations, and I will gather them from all sides and bring them into their land. And I will make them one nation in that land, in the mountains of Israel. And one king will rule over them all, and they will no longer be two nations. And they will never again be divided into two kingdoms.” (Note that this Haftorah is just between the Haftorah of Shabbat Chol Hamoed Pesach, about the dried bones, and the Haftorah of Shabbat Sukkot, about the war of Gog and Magog). Based on these verses, there is a tradition that at the end of days there will be two Mashiachs (anointed ones) - Mashiach ben David and Mashiach ben Yosef, or ben Ephraim (see the detailed discussion by Rav Yitzchak Isaac Chaver in Siach Yitzchak, vol. 2, chapter Veshalach).