  We report results from a search for neutrino-induced neutral current (NC)
resonant $\Delta$(1232) baryon production followed by $\Delta$ radiative decay,
with a $\langle0.8\rangle$~GeV neutrino beam. Data corresponding to
MicroBooNE's first three years of operations (6.80$\times$10$^{20}$ protons on
target) are used to select single-photon events with one or zero protons and
without charged leptons in the final state ($1\gamma1p$ and $1\gamma0p$,
respectively). The background is constrained via an in-situ high-purity
measurement of NC $\pi^0$ events, made possible via dedicated $2\gamma1p$ and
$2\gamma0p$ selections. A total of 16 and 153 events are observed for the
$1\gamma1p$ and $1\gamma0p$ selections, respectively, compared to a constrained
background prediction of $20.5 \pm 3.65 \text{(sys.)} $ and $145.1 \pm 13.8
\text{(sys.)} $ events. The data lead to a bound on an anomalous enhancement of
the normalization of NC $\Delta$ radiative decay of less than $2.3$ times the
predicted nominal rate for this process at the 90% confidence level (CL). The
measurement disfavors a candidate photon interpretation of the MiniBooNE
low-energy excess as a factor of $3.18$ times the nominal NC $\Delta$ radiative
decay rate at the 94.8% CL, in favor of the nominal prediction, and represents
a greater than $50$-fold improvement over the world's best limit on
single-photon production in NC interactions in the sub-GeV neutrino energy
range
