Trisection genus invariance for exotic smooth 4-manifolds

Let $X$ and $Y$ be smooth $4$-manifolds, and let $g(X)$ and $g(Y)$ denote their trisection genera, namely the minimal genera of the triple-intersection surfaces among (relative) trisections of the manifolds. The manifolds are exotic if they are homeomorphic but not diffeomorphic.

Trisection genus invariance conjecture. If two smooth $4$-manifolds $X$ and $Y$ are exotic, then

$$g(X)=g(Y).$$

This would make trisection genus a homeomorphism invariant of smooth $4$-manifolds, conditional on the additivity conjectures for trisection genus under connected sum and boundary connected sum. The source does not establish the conjecture.