the Egyptians took over again and expelled them all.

Manetho and Josephus claim that the Hyksos were expelled, but there is no archeological evidence for this (MUCH LIKE LE EXODUS! ), and quite the opposite, in fact the Hyksos, and Semites in general remained in Egypt well after they were overthrown:

Although Manetho indicates that the Hyksos population was expelled to the Levant, there is no archaeological evidence for this, and Manfred Bietak argues on the basis of archaeological finds throughout Egypt that it is likely that numerous Asiatics were resettled in other locations in Egypt as artisans and craftsmen.[111] Many may have remained at Avaris, as pottery and scarabs with typical "Hyksos" forms continued to be produced uninterrupted throughout the Eastern Delta.[74] Canaanite cults also continued to be worshiped at Avaris.[112]

the Joseph story from the Genesis is likely a collective memory of the Hyksos rule right? I read it is possible the Exodus could have some basis on the Hyksos expulsion as well.

From a non-religious POV, yes, even atheistic scholars these days admit that there is a historical basis for the Exodus, even if it is hagiographic and exaggerated for political and religious purposes like the Trojan War, !historychads !christians !catholics !jidf I already wrote a three big comments summarizing arguments in favor of the historicity of the Exodus, from a non-Religious Fundamentalist "THE TRUTH IS OUT THERE TRUST THE PLAN PATRIQTS " schizo pseudohistory, it is very possible for you to argue for the historicity of the Exodus with a Fact-Checked Good Faith Peer-Reviewed Science-Affirming Evidence-Filled PhD. Egyptological perspective:

https://rdrama.net/post/286191/wikiposters-discuss-the-historical-merits-of/6733901#context

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Genesis 50:

25 So Joseph made the Israelites swear, saying, "When God comes to you, you shall carry up my bones from here."

Joseph 24:

32 The bones of Joseph, which the Israelites had brought up from Egypt, were buried at Shechem, in the portion of ground that Jacob had bought from the children of Hamor, the father of Shechem, for one hundred pieces of money; it became an inheritance of the descendants of Joseph.

https://www.biblicalarchaeology.org/daily/news/the-expulsion-of-the-hyksos/

I don't think it's conclusive or especially well grounded as a theory, the Hyksos traditionally were associated with Phoenicians as well IIRC. Anyway, the Bible does contradict that theory which would mean I'd want strong evidence. !Catholics