The similarity-degree conjecture for Fourier algebras

Let $G$ be a locally compact group. Write $\widetilde{\mathrm{A}}(G)_1$ for the unit ball of the unitization of the Fourier algebra $\mathrm{A}(G)$, let $\mathcal{C}_0(G)$ denote the algebra of continuous functions vanishing at infinity, and let $d_{\mathrm{cb}}(\mathrm{A}(G))$ be the completely bounded similarity degree of $\mathrm{A}(G)$. Similarity-degree conjecture. For every locally compact group, one has

$$\widetilde{\mathrm{A}}(G)_1\cong\mathcal{C}_0(G)\quad\text{and}\quad d_{\mathrm{cb}}(\mathrm{A}(G))\leq 2.$$

The claim gives a uniform upper bound on the completely bounded similarity degree of Fourier algebras and identifies the relevant unitized object with $\mathcal{C}_0(G)$. The supplied text does not indicate whether this assertion is established or remains open.