  The special Buchdahl-inspired metric obtained in a recent paper [Phys. Rev. D
107, 104008 (2023)] describes asymptotically flat spacetimes in pure
$\mathcal{R}^{2}$ gravity. The metric depends on a new (Buchdahl) parameter
$\tilde{k}$ of higher-derivative characteristic, and recovers the Schwarzschild
metric when $\tilde{k}=0$. It is shown that the special Buchdahl-inspired
metric supports a two-way traversable Morris-Thorne wormhole for
$\tilde{k}\in(-1,0)$ in which case the Weak Energy Condition is formally
violated, a naked singularity for $\tilde{k}\in(-\infty,-1)\cup(0,+\infty)$,
and a non-Schwarzschild structure for $\tilde{k}=-1$.
