Quasi-$F$-split primitive symplectic varieties in positive characteristic

Let $X$ be the good reduction of a projective hyperkähler variety of dimension $2n\geq4$. We prove that $X$ is quasi-$F$-split if and only if it is Frobenius split, equivalently if $\operatorname{H}^2_{\operatorname{crys}}(X/W)[1/p]$ has a slope-zero part. Thus its quasi-$F$-split height is $1$ or $