Then mathematician's uncertainty was such that they would have causal graphs with TSW causing FLT.

Well the direction of the arrow would be unspecified. After all, not FLT implies not TSW is equivalent to TSW implies FLT, so there's a symmetry here. This often happens in causal modelling; many causal discovery algorithms can output that they know an arrow exists, but they are unable to determine its direction.

Also, conjectures are the causes of their proofs rather than vice versa. You can see this as your degrees of belief in the correctness of purported proofs are independent given that the conjecture is true (or false), but dependent when the truth-value of the conjecture is unknown.

Apart from this detail, I agree with your comment and I find it to be similar to the way I think about the causal structure of math.