The Haggada famously compares God's treatment of the Egyptians during the plagues to they way He later dealt with them at the Sea:
"In Egypt what was said? 'And the sorcerers said to Paro, this is the figure of God' (Shemos 8:15) [but] at the Sea it says: 'And the Jews saw the great hand that God brought against Egypt' (Shemos 14:31)...With how many plagues were they hit with [just one] finger? 10 plagues. From here we can say that in Egypt they were hit with 10 plagues, and on the Sea they were hit with 50 plagues..."
The source of that passage seems to be Mekhilta DeRabbi Yishmael Beshalach #7.
One might be tempted to assume that "finger" is a precise representation of God's involvement in the Egyptian plagues, while "hand" uniquely characterizes His treatment of the Egyptian army at the Sea. But that would ignore some important details:
The word "finger" is used in the context of only one of the ten plagues (lice) and was the word chosen by Paro's sorcerers - hardly a reliable Torah source.
The word "hand" is actually also used prominently in the context of the plagues in Egypt, both in relation to the plague of pestilence (דבר - Shemos 9:3) and in God's introduction to the plagues (Shemos 7:4-5).
So the use of the "finger"/"hand" relationship as part of a traditional logical device to calculate the numeric relationship between God's treatment of Egyptians across both locations would seem unlikely.
But I think the bigger problem with a simplistic reading of this passage is that there doesn't seem to be any way to know what those 50, 200, or 250 plagues at the Sea actually were. The Torah certainly doesn't tell us, and I'm aware of no source from the Tanaaim or Amoraim offering any greater detail.
So what value is there in reading those numbers each year if, for one thing, we have no idea what they represent, and if the direct linguistic distinction on which those numbers are based is neither unique nor representative?
I won't claim to have a spectacular solution. But I will suggest that the Midrash isn't trying to deliver a history lesson. Instead, it chose to focus specifically on the sorcerers' admission of helplessness because that marked the start of an important development in the realization of God's plan for the education of both Egyptians and Jews. The focus on "hand" at the Sea could serve to evoke the potential of that event to inspire a recognition of God's power that's both greater and longer-lasting than whatever we experienced until that point.
The alternate numbers offered by Rabbi Eliezer (5x40) and Rabbi Akiva (5x50) might be intended to evoke their own implicit connections. Although I'm certainly not going to offer any guesses as to what those connections might be.
But however you choose to understand this particular passage, there's certainly never a substitute for thoughtful analysis.
Regarding the sorcerers not being a “Torah source”, if it’s in the Torah it’s a Torah source. They also didn’t speak Biblical Hebrew-they might have said something similar to that but if it’s written in the Torah-it’s a trusted source.
Regarding the plagues-I’ll give you an example: how many plagues was COVID ? It was one plague but had a major impact on every sector-There were 10 plagues in Egypt and 10 at the sea, what’s being counted is the impact it had, the magnitude of each plague.
Even if we are at a complete loss to know what those numbers might mean, the dominant trend of our age seems to demand that we regard any non-literal interpretation of either תורה שבכתב or תורה שבעל פה with extreme suspicion!