Moshkovitz–Shapira's lower-bound conjecture for bipartite saturation

Let $1\le s\le t$ be integers. A bipartite graph is $K_{s,t}$-saturated if it contains no copy of $K_{s,t}$, but adding any missing edge between its color classes creates a copy of $K_{s,t}$. Moshkovitz–Shapira's conjecture. There is an $n_0$ such that, whenever $n\ge n_0$, every $K_{s,t}$-saturated $n$-by-$n$ bipartite graph $G$ contains at least

$$(s+t-2)n-\left\lfloor\left(\frac{s+t-2}{2}\right)^2\right\rfloor$$

edges. This is the proposed additive-constant comparison with the ordered saturation number; the paper notes that the bound is tight by construction. The claim remains open in general, with the first open case being $s=2$ and $t=3$.