  We present a state sum construction that assigns a scalar to a skeleton in a
closed oriented three-dimensional manifold. The input datum is the pivotal
bicategory $\mathbf{Mod}^{\mathrm{sph}}(\mathcal{A})$ of spherical module
categories over a spherical fusion category $\mathcal{A}$.
  The interplay of algebraic structures in this pivotal bicategory with moves
of skeleta ensures that our state sum is independent of the skeleton on the
manifold. We show that the bicategorical invariant recovers the value of the
standard Turaev-Viro invariant associated to $\mathcal{A}$, thereby proving the
independence of the Turaev-Viro invariant under pivotal Morita equivalence
without recurring to the Reshetikhin-Turaev construction.
  A key ingredient for the construction is the evaluation of graphs on the
sphere with labels in $\mathbf{Mod}^{\mathrm{sph}}(\mathcal{A})$ that we
develop in this article. A central tool are Nakayama-twisted traces on pivotal
bimodule categories which we study beyond semisimplicity.
