Weight-additivity conjecture for weakly separated tableaux

Let $T \in \operatorname{SSYT}(2,[n])$ have $m$ columns. Let $(S_1,\ldots,S_m)$ be the unique unordered $m$-tuple of pairwise weakly separated one-column tableaux whose union is $T$. For a tableau $R$, let $\operatorname*{wt}_R$ denote the weight of the positroidal subdivision corresponding to $R$. Weight-additivity conjecture. Then

$$\operatorname*{wt}_T=\operatorname*{wt}_{S_1}+\cdots+\operatorname*{wt}_{S_m}.$$

This would express the subdivision weight of every tableau in $\operatorname{SSYT}(2,[n])$ as the sum of the weights of its canonical one-column decomposition; the source presents it as a belief following the split-subdivision result.