Varbaro's depth and local cohomological dimension conjecture

Let $R$ be a regular local ring containing a field, and let $I$ be an ideal of $R$. Varbaro's conjecture. If

$$\operatorname{depth}(R/I)\geq 3,$$

then

$$\operatorname{lcd}_R(I)\leq \dim(R)-3.$$

This extends the known characteristic-independent cases of the depth–local-cohomological-dimension implication; the source says that the case in question was not completely settled there.