If $\mathscr{X}/R$ is a toric model of $X=\mathbb{T}$, it follows from Proposition 1.5.2 that the Berkovich retraction:

$$\rho_{\mathscr{X}}:\widehat{\mathscr{X}}_{\eta}\longrightarrow\Sk(\mathscr{X})$$

is an affinoid torus fibration over the interior of $\Sk(\mathscr{X})$. This also holds when $X$ is a regular proper toric variety over $K$, and $\mathscr{X}$ a regular proper toric model, by [GJKM19, Theorem A.4].