\begin{abstract}
Let $G$ be a simply connected semisimple complex algebraic group, and let
$U_P$ be the unipotent radical of a parabolic subgroup $P\subseteq G$.
We prove that the affinization $\overline{T^*(G/U_P)}$ is factorial and
has terminal symplectic singularities. To establish symplectic
singularities, we apply a criterion of Fu--Liu after constructing a log
Fano boundary on an associated projective bundle over the full flag
variety. The boundary construction uses Frobenius splitting of flag
varieties and reduction modulo primes to obtain log canonicity in
characteristic zero. We then prove that every first-order Poisson
deformation of $\overline{T^*(G/U_P)}$ is trivial. Namikawa's deformation
theory implies that the singular locus has codimension at least four,
yielding terminality. No conical grading is assumed.
\end{abstract}