  We categorify various finite-type cluster algebras with coefficients using
completed orbit categories associated to Frobenius categories. Namely, the
Frobenius categories we consider are the categories of finitely generated
Gorenstein projective modules over the singular Nakajima category associated to
a Dynkin diagram and their standard Frobenius quotients. In particular, we are
able to categorify all finite-type skew-symmetric cluster algebras with
universal coefficients and finite-type Grassmannian cluster algebras. Along the
way, we classify the standard Frobenius models of a certain family of
triangulated orbit categories which include all finite-type $n$-cluster
categories, for all integers $n\geq 1$.
