  We consider a twist $E$ over an \'etale groupoid $G$. When $G$ is principal,
we prove that the nuclear dimension of the reduced twisted groupoid
$\mathrm{C}^*$-algebra is bounded by a number depending on the dynamic
asymptotic dimension of $G$ and the topological covering dimension of its unit
space. This generalizes an analogous theorem by Guentner, Willett, and Yu for
the $\mathrm{C}^*$-algebra of $G$. Our proof uses a reduction to the unital
case where $G$ has compact unit space, via a construction of ``groupoid
unitizations'' $\widetilde{G}$ and $\widetilde{E}$ of $G$ and $E$ such that
$\widetilde{E}$ is a twist over $\widetilde{G}$. The construction of
$\widetilde G$ is for r-discrete (hence \'etale) groupoids $G$ which are not
necessarily principal. When $G$ is \'etale, the dynamic asymptotic dimension of
$G$ and $\widetilde{G}$ coincide. We show that the minimal unitizations of the
full and reduced twisted groupoid $\mathrm{C}^*$-algebras of the twist over $G$
are isomorphic to the twisted groupoid $\mathrm{C}^*$-algebras of the twist
over $\widetilde{G}$. We apply our result about the nuclear dimension of the
twisted groupoid $\mathrm{C}^*$-algebra to obtain a similar bound on the
nuclear dimension of the $\mathrm{C}^*$-algebra of an \'etale groupoid with
closed orbits and abelian stability subgroups that vary continuously.
