The rectangular Delta conjecture for decorated Dyck paths

Let $m,n\in\mathbb{N}$, let $e_{m,n}$ be the rectangular Dyck-path symmetric function, and let $\Theta_{e_k}$ be the Theta operator indexed by $e_k$. For $\pi\in\mathsf{LRD}(m+k,n+k)^{\ast k}$, let $\mathsf{area}(\pi)$ be its area statistic and $x^\pi$ its monomial weight. Rectangular Delta conjecture. For any $m,n\in\mathbb{N}$,

$$\left.\Theta_{e_k}e_{m,n}\right\rvert_{q=1}=\sum_{\pi\in\mathsf{LRD}(m+k,n+k)^{\ast k}}t^{\mathsf{area}(\pi)}x^\pi.$$

This is a univariate rectangular analogue of the rise version of the Delta conjecture, with $k$ decorated rises. The source reports computer verification up to semiperimeter $13$ and presents the formula as a conjecture; no general proof is supplied in the given text.