The diagonal-maximality conjecture for correspondence packing of complete bipartite graphs

For positive integers $a$ and $b$ with $a>b$, let $K_{a,b}$ denote the complete bipartite graph with parts of sizes $a$ and $b$, and let $\chi_c^\star$ denote its correspondence packing number. Diagonal-maximality conjecture.

$$\chi_c^\star(K_{a+1,b})\le \chi_c^\star(K_{a,b+1}).$$

Thus, among complete bipartite graphs with a fixed total number of vertices, the maximum value is conjectured to occur on the diagonal, in the sense stated above. The source notes that this is analogous to a belief about Ramsey numbers and is also expected for the list and correspondence colouring parameters; no resolution is supplied.