Dao's theta-pairing vanishing conjecture for even-dimensional isolated singularities

Let $(R,\mathfrak{m})$ be a local ring whose completion $\widehat R$ is a hypersurface in an unramified regular local ring. Assume that $R$ is an even-dimensional isolated singularity. Here $\theta^R(-,-)$ denotes Dao's theta pairing. Dao's conjecture.

$$\theta^R(-,-)=0.$$

The vanishing forces rigidity under the theorem recalled in the source. The graded version was proved by Moore, Piepmeyer, Spiroff, and Walker, but the stated general conjecture is presented as an active question.