Finiteness conjecture for regular weak Hopf algebras

Let $H$ be a finite-dimensional weak Hopf algebra satisfying

$$S^2=\operatorname{id}\quad\text{{\rm on the minimal weak Hopf subalgebra }}H_{\mathrm{min}}\text{{\rm of }}H.$$

Finiteness conjecture. In any given dimension, the number of non-isomorphic weak Hopf algebras $H$ with this property is finite.

The property is a natural regularity condition preserved by duality and can be achieved by deformation. The source does not state whether this finiteness assertion has been proved or disproved.