Rigidity conjecture for skew braces with non-abelian characteristically simple multiplicative group

Let $(B,+,\cdot)$ be a skew brace, meaning that $(B,+)$ and $(B,\cdot)$ are groups on the same set and the skew-brace compatibility law holds. Assume that $S$ is a finite non-abelian simple group and $n\geq 1$ is an integer such that

$$(B,\cdot)\cong S^n.$$

Rigidity conjecture. Then

$$(B,+)\cong (B,\cdot).$$

This conjecture asserts that a skew brace with non-abelian characteristically simple multiplicative group has no substantially different additive group. The corresponding rigidity is motivated by known results for simple and quasisimple multiplicative groups and by a Lie-theoretic analogue, while the conjecture itself remains open.