  There are two main types of objects in the theory of cluster algebras: the
upper cluster algebras ${{\boldsymbol{\mathsf U}}}$ with their
Gekhtman-Shapiro-Vainshtein Poisson brackets and their root of unity
quantizations ${{\boldsymbol{\mathsf U}}}_\varepsilon$. On the Poisson side, we
prove that (without any assumptions) the spectrum of every finitely generated
upper cluster algebra ${{\boldsymbol{\mathsf U}}}$ with its GSV Poisson
structure always has a Zariski open orbit of symplectic leaves and give an
explicit description of it. On the quantum side, we describe the fully Azumaya
loci of the quantizations ${{\boldsymbol{\mathsf U}}}_\varepsilon$ under the
assumption that ${{\boldsymbol{\mathsf A}}}_\varepsilon = {{\boldsymbol{\mathsf
U}}}_\varepsilon$ and ${{\boldsymbol{\mathsf U}}}_\varepsilon$ is a finitely
generated algebra. All results allow frozen variables to be either inverted or
not.
