Mal'tsev products for proper regular groupoid varieties

Determine whether, for every proper regular variety V of groupoids (magmas), the Mal'tsev product V ∘ S with the semilattice variety S fails to be a variety.

Background

Building on the commutative groupoid case, where CG ∘ S is shown not to be a variety, the authors consider whether this phenomenon extends to all proper regular subvarieties of the variety of all groupoids.

The question targets the general behavior of Mal'tsev products with S in the regular (i.e., only regular identities) groupoid setting, asking if equational closure fails universally for proper regular varieties.