The visibility-dimension claim for the abelian surface 9603.2.a.o

Let $A/\mathbb{Q}$ be the abelian surface with label $\textnormal{\texttt{9603.2.a.o}}$. Its Tate--Shafarevich group $\Sha(A/\mathbb{Q})$ contains an element of order $7$.

Visibility-dimension claim. This element is not visible in any abelian threefold; in particular, its visibility dimension is $4$.

This claim concerns the minimum dimension of an abelian variety over $\mathbb{Q}$ that makes a given element of the Tate--Shafarevich group visible. The supplied text gives no evidence that the claim has been resolved.