  Let $G$ be a connected reductive group over a finite extension of
$\mathbb{Q}_p$. We show that for each $b \in B(G)$, the strongly regular locus
of the inertia stack of $\mathrm{Bun}_G^b$ is open in the inertia stack of
$\mathrm{Bun}_G$. As a consequence, we extend the computation of
Hansen--Kaletha--Weinstein of trace distributions of the cohomology of local
shtuka spaces $\mathrm{Sht}_{G,b,\mu}$ to non-basic $b$ and in some cases
beyond the elliptic locus. If $b$ is closed in $B(G,\mu)$, then we compute the
trace distribution of the entire strongly regular locus.
