Significant Find by the Israel Antiquities Authority

[Confused Ape]

That's the problem. The period of time when Judah and Egypt would have been competitors was exceedingly short. Babylon revolted against Assyria in 626 BC and 10 years later had evicted them from Babylonia. Four years later, in 612 BC, Nineveh was sacked and destroyed. The 26th Dynasty of Egypt, formerly Assyrian vassals themselves, stayed loyal and joined the Assyrians in an effort to stop the Babylonians. The Assyrians were forced to move their capital to Haran and to concentrate their military force remaining to protect their capital. This left the northern areas of Palestine open to Judahite dreams of glory but it was also the former seat of the Egyptian empire in Canaan.

Folk tradition doesn't follow an established historical timeline, though.

Sharuhen

Sharuhen was an ancient town in the Negev Desert. Following the expulsion of the Hyksos from Egypt in the second half of the 16th century BCE, they fled to Sharuhen and fortified it. The armies of Pharaoh Ahmose I seized and razed the town after a three-year siege.

It's unlikely that every single Hyksos was killed so the survivors would have ended up mingling with the local population.

Canaanite folklore - we were once ruled by Pharoah.

Hyksos folklore - we were once chased out of Egypt by Pharoah.

Put them together and it ends up as the Israelite myth of - we were once in Egypt and were chased by Pharoah while we were leaving.

Then there's the Ipuwer Papyrus

The Ipuwer Papyrus is a single papyrus holding an ancient Egyptian poem, called The Admonitions of Ipuwer[1] or The Dialogue of Ipuwer and the Lord of All.[2] Its official designation is Papyrus Leiden I 344 recto.[3] It is housed in the Dutch National Museum of Antiquities in Leiden, Netherlands, after being purchased from Giovanni Anastasi, the Swedish consul to Egypt, in 1828. The sole surviving manuscript dates to the later 13th century BCE (no earlier than the 19th dynasty in the New Kingdom).

The Ipuwer Papyrus describes Egypt as afflicted by natural disasters and in a state of chaos, a topsy-turvy world where the poor have become rich, and the rich poor, and warfare, famine and death are everywhere. One symptom of this collapse of order is the lament that servants are leaving their servitude and acting rebelliously.

Nobody really knows what it's about but there are several theories.

The date for the composition of this document is unknown. The papyrus itself (Papyrus Leiden I 344) is a copy made during the New Kingdom of Egypt.[1] The dating of the original composition of the poem is disputed, but several scholars have suggested a date between the late 6th dynasty and the Second Intermediate Period (ca. 1850 BCE-1600 BCE),[4] and appears to describe how the Hyksos took over Egypt.[5][6]

Another theory suggests this -

Further assessment of the text reads:

"It is quite likely that the destruction lament in the 'Admonitions' refers to the destruction of Memphis at the end of the Old Kingdom. Thus, this fully independent micro-text can be understood as a sort of oral tradition or at least a literarily formed piece of historical recollection which has trickled into writing, but it is clearly a text with literary forms and ambitions – certainly not a historical report in the narrower sense. Indeed, even recently this passage has been understood as an almost concrete historical report.[21]

Egyptian folklore about past disasters could have spread to Canaan when it was part of the Egyptian empire. It then got mixed into the Israelite folklore so they became the servants who left.

Ancient Egyptian Servants

Some servants were assigned to work for the pharaoh. They reported to the royal controller who was in charge of the pharaoh's servants. The servants worked as cooks, butlers, litter carriers, and as pharaoh's dressers. The male servants also worked on royal building projects or were sent to fight in the Egyptian army.

It doesn't take much for servants working on building projects to be turned into slaves.