Complete bipartite even-cycle partite saturation conjecture

Let $K_{n_1,n_2}$ be a complete bipartite graph, and let $C_{2\ell}$ denote the cycle of length $2\ell$. Even-cycle bipartite saturation conjecture. For $\ell\geq 4$ and $n_1,n_2\geq \ell+2$,

$$sat(K_{n_1,n_2},C_{2\ell})=n_1+n_2+\ell^2-3\ell+1.$$

This conjecture addresses the exact partite saturation number for sufficiently large bipartite parts. The supplied text gives no resolution evidence.