There was an exodus of peoples from Egypt toward what we think of as the Jewish promised land, some of whome became the jews of today. But it took place over generations, not in one fell swoop as the fable would have one think, and they weren't a cohesive self-identified people. The character of Moses... eh, doubtful. Maybe there was some folklore once with a kernel of fact-basis. Does it even matter?

No. The archeological record explains it well enough as watchman notes.

Well i have studied well the exodus story and it is clear that there are lies and exaggerations in it.
That does not mean that it is not founded in historical events.

One video which looks at the exodus claims and checks for evidence to support those claims is:
https://www.youtube.com/watch?v=sawWSvHjqEE
However one must point out that this is just once sided, after personally analyzing most of these claims, some things are exaggerated to the point of ridicule in this video.(burning bush retain it's shape(please!!).)
EG: Jews were not slaves, yes they had slaves and the Egyptians had Jewish slaves, but the Jews had rich people that were not slaves, they indeed traded and became part of Egyptian culture at some point.
They also followed their traditions which Yahweh seem to hate in the bible, BTW they were not JEWS at this point, they became Jews AFTER Yahweh grouped them together with others according to the bible.
They were immigrants from Sumer and decedents of Abraham and his family.

Also there seem to be some natural explanations for most of the "miraculous" events.
except: pillar of clouds and pillar of fire during the day and the parting of waters +others.

The plagues can be explained by the complete lack of reason why such events happen in that way.
The order of the plagues are the same order of events that would happen if something like a huge eruption somewhere close by just happened.
It just happens that the Santorini volcano erupted around 1628 BC but the exodus happened around 1450 BC thus one can see that maybe the Jewish writers just inserted such a disaster in the story to make the pharaoh look bad.

OR maybe it actually happened again artificially by someone who understood how the disaster happened many years later after the fact.
Moses being a son of pharaoh had all the education need to understand what happened and why.
You poison the waters and basically you get very similar effects in a place which is so dependent on water.
Then god did not do the plagues, but Moses had knowledge of the effects and tricked the Egyptians.

OR simply there is some knowledge that we do not know that would explain all this.

Long answer.... not everything is BS, there might have been elements of truth.

There is surly not enough evidence to make the story reliable.
We do not even know for sure who killed JFK to this day and it is not 3000 Years ago.
The jews are writing biased and inspiring history for them, so are other historical accounts that we have which do not have contemporary accounts.
You might be shocked if you check how much in history we do not have contemporary accounts.

I however remain skeptical about it being all made up because there are some stories/episodes which do not make the Jews look good.
Like for example; when Yahweh steps on someone's shit and he is so pissed that he makes them write down in the bible the instructions of how to do toilet.(funny)

That would not make much sens as a Jewish invention, makes more sens that something like that really happened and the Jews were forced to record it.