Actually happened that way. I tend to believe both happened but whethere they both did or not they have powerful meanings to them.

proclaimed for centuries.

but that myth (an archetypal narrative--not a fairy tale) has accreted around it.

The author of the article references one such. During the seventeenth dynasty, a people from Canaan had settled in the Nile Delta and the areas immediately south. We know them today as the Hyksos. They established themselves as rulers of Lower (northern)Egypt and demanded fealty from Upper (southern) Egypt, then ruled by the Tao family. Sequenenre Tao raised an army to recapture the north, but was killed in battle. His two sons, Kamose and Ahmose, completed his work, and the Hyksos were forced out. So we have here a departure of a Canaanite people from Egypt, but it was the rulers, not the slaves; it was a rout, not a triumphant escape. This sequence of events may give the Moses story its narrative structure.

However.

There are some very odd things about the story in Exodus. One is the name Moses. It's not "an Egyptian name," it's half an Egyptian name. It means roughly "has given a child" and is usually preceded by the name of a god--thus Ptahmose, Ramose (Rameses), Thutmose, etc. Dropping the god's name might be something an Egyptian would do if he converted to a foreign, more or less monotheistic faith whose god's name was mysterious or not to be spoken.

A second, extrememely odd thing is the incident in the story in which Moses flees Egypt because he has killed an Egyptian overseer. Here's the situation: Moses is presented as the (adopted) son of Pharaoh's daughter, whose husband is never mentioned. Because there is no other adoptive father, this part of the narrative may reflect a practice of the eighteenth dynasty according to which the Pharaoh married one of his own daughters with the intention of maintaining the matrilineal bloodline unbroken. We know that both Amenhotep III and his son Akhenaten followed this custom. This places Moses in the position of eldest son of the King and heir to the throne.

And he's going to run away because he killed a commoner, more likely a slave? It would be regarded as poor taste at worst, not a capital crime.

We also know that Akhenaten introduced near-monoteism to Egypt. (He and his family were worshipped along with the god Aten.) So here's something that seems plausible to me. Perhaps a charismatic eighteenth-dynasty Egyptian brought the faith of the Aten into Canaan, where he dropped the prefix of his name or the people who later told his story did. When Atenism collapsed, some of its followers remained in Canaan because they would in fact have been repudiated if they returned to an Egypt whose priesthood was bent on erasing Akhenaten, his capital and his religion from history. Alternatively, that faith may have made a considerable number of converts among the native Canaanites. Or both scenarios may be true. In any event, the worship of Aten gradually morphed into the cultus of Yahweh, and, much later, from there into Judaism.

One thing is clear. Akhenaten was not Moses, though Judith Tarr as written an enormously entertaining novel around the premise. (Pillar of Fire.) Akhenaten's grave (KV-55) was discovered in the early 20th., century, but it was not known until very recently that Akhenaten was actually buried in it. Modern DNA analysis establishes the otherwise anonymous occupant
of KV-55 as Tutankhamen's father, as well as the full brother of the mummy known as the Younger Lady and the son of Queen Tiye, the so-called Elder Lady. He died and was buried in Egypt. He is clearly linked to Judaism, though. His beautiful "Hymn to the Aten" is incorporated into Psalm 107 as a song of praise to Yahweh, the One God who displaced his own.