Symmetric monoidality of relative norms

Let $G$ be a compact Lie group, let $H<G$ be a closed subgroup, and let $X$ and $Y$ be $H$-equivariant $\mathcal{D}_V$-algebras whose underlying $H$-equivariant orthogonal spectra are cofibrant in the $U_H$-universe model structure. Relative norm monoidality conjecture. There is a natural $U$-universe $G$-equivariant weak equivalence

$$N_H^G X\wedge N_H^G Y\simeq N_H^G(X\wedge Y).$$

This predicts that the relative norm preserves smash products on the stated cofibrant inputs, as expected from symmetric monoidality of factorization homology.