  For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a
non-trivial minuscule representation and a connected marked surface $\Sigma$
with at least two marked points and no punctures, we prove that the cluster
algebra $\mathscr{A}_{\mathfrak{g},\Sigma}$ associated with the pair
$(\mathfrak{g},\Sigma)$ coincides with the upper cluster algebra
$\mathscr{U}_{\mathfrak{g},\Sigma}$. The proof is based on the fact that the
function ring $\mathcal{O}(\mathcal{A}^\times_{G,\Sigma})$ of the moduli space
of decorated twisted $G$-local systems on $\Sigma$ is generated by matrix
coefficients of Wilson lines introduced in [IO20]. As an application, we prove
that the Muller-type skein algebras $\mathscr{S}_{\mathfrak{g},
\Sigma}[\partial^{-1}]$ [Muller,IY23,IY22] for $\mathfrak{g}=\mathfrak{sl}_2,
\mathfrak{sl}_3,$ or $\mathfrak{sp}_4$ are isomorphic to the cluster algebras
$\mathscr{A}_{\mathfrak{g}, \Sigma}$.
