Edge-only orbit coloring symmetry-fafulness conjecture

Let $P$ be a full-dimensional polytope of dimension $d\geq 3$, with edge-graph $G_P$. Consider the edge-only orbit coloring, obtained by coloring edges according to their orbits under the relevant symmetry group. A coloring is symmetry faithful when every automorphism of the colored edge-graph is induced by a symmetry of $P$.

Edge-only orbit coloring conjecture. The edge-only orbit coloring is symmetry faithful for both the linear symmetry group and the orthogonal symmetry group:

$$\operatorname{Aut}(G_P^{\mathrm{edge\text{-}only\ orbit\ coloring}})=\operatorname{Aut}_{\operatorname{GL}}(P)$$

and

$$\operatorname{Aut}(G_P^{\mathrm{edge\text{-}only\ orbit\ coloring}})=\operatorname{Aut}_{\operatorname{O}}(P).$$

This proposes that, in dimension at least three, edge colors alone suffice to capture both linear and orthogonal symmetries of a polytope. The supplied text does not state whether the claim is known or resolved, so its status remains open.