Graph localization and $G$-infinity-operads conjecture

Let $G$ be a finite group, let $(\operatorname{sOp}^{\operatorname{col}})^G$ be the category of $G$-objects in simplicial coloured operads, and let $G$-$\infty$-$\operatorname{Op}$ denote the corresponding category of $G$-$\infty$-operads. Graph localization and $G$-infinity-operads conjecture. The Dwyer–Kan localization of $(\operatorname{sOp}^{\operatorname{col}})^G$ at the graph weak equivalences is equivalent to the subcategory of $G$-$\infty$-$\operatorname{Op}$ spanned by the $G$-$\infty$-operads whose equivariant space of colours has a $G$-set of connected components, via $\operatorname{Set}^G\hookrightarrow\operatorname{Psh}({\mathscr{O}}_G)$. This is the final comparison predicted by combining the preceding three conjectures; the source presents it as a proposed consequence and gives no proof or resolution.