Lascoux atom formula conjecture via set-valued skyline tableaux

Let $w$ be a permutation and $\lambda$ a partition, and let $\operatorname{SLT}_{w\lambda}$ be the set of semistandard set-valued skyline tableaux of shape $w\lambda$. Define the Lascoux atom by

$$\overline{L}_{w\lambda}(\mathbf{x};\beta):=\overline{\varpi}_w x^{\lambda},$$

where $\overline{\varpi}_i=\varpi_i-1$. Lascoux atom formula conjecture. One has

$$\overline{L}_{w\lambda}=\sum_{S\in\operatorname{SLT}_{w\lambda}}\operatorname{wt}_{\beta}(S).$$

This proposes a tableau-generating-function interpretation for Lascoux atoms, paralleling the conjectural combinatorial formulas for Lascoux polynomials.