The orthosymplectic tensor-power conjecture for the quotient enveloping algebra

Let $U$ be the superspace equipped with its nondegenerate quadratic element $\omega$, let $E$ be a vector space of dimension $n$, and set

$$\mathfrak{g}'_{U,E}=(U\otimes E)\oplus S^2E.$$

The elements of $S^2E$ are central, and the bracket on $U\otimes E$ is defined by

$$[u\otimes e,u'\otimes e']=\omega(u,u')ee'.$$

Let $I'$ be the left ideal in the enveloping algebra $\mathrm{U}(\mathfrak{g}'_{U,E})$ generated by the naturally embedded subspace $\bigwedge^2E$, and define

$$Z'_{U,E}=\mathrm{U}(\mathfrak{g}'_{U,E})/I'.$$

Let $C=\bigwedge^\bullet(U)/(\omega)$. The orthosymplectic tensor-power conjecture. There is an $\mathbf{Sp}\mathbf{O}(U)$-equivariant isomorphism

$$Z'_{U,E}\cong C^{\otimes n}.$$

In particular,

$$\mathrm{H}\mathrm{S}(Z'_{U,E})=\mathrm{H}\mathrm{S}(C)^n.$$

This conjecture is the proposed analogue, for the orthosymplectic setting, of the paper's main theorem concerning good functorial properties. The source explicitly says that the authors do not know how to prove this analogue, so its resolution remains open.