  A search for a chargino$-$neutralino pair decaying via the 125 GeV Higgs
boson into photons is presented. The study is based on the data collected
between 2015 and 2018 with the ATLAS detector at the LHC, corresponding to an
integrated luminosity of 139 fb$^{-1}$ of $pp$ collisions at a centre-of-mass
energy of 13 TeV. No significant excess over the expected background is
observed. Upper limits at 95% confidence level for a massless
$\tilde{\chi}^{0}_{1}$ are set on several electroweakino production
cross-sections and the visible cross-section for beyond the Standard Model
processes. In the context of simplified supersymmetric models, 95%
confidence-level limits of up to 310 GeV in
$m(\tilde{\chi}^{\pm}_{1}/\tilde{\chi}^{0}_{2})$, where
$m(\tilde{\chi}^{0}_{1})=0.5$ GeV, are set. Limits at 95% confidence level are
also set on the $\tilde{\chi}^{\pm}_{1}\tilde{\chi}^{0}_{2}$ cross-section in
the mass plane of $m(\tilde{\chi}^{\pm}_{1}/\tilde{\chi}^{0}_{2})$ and
$m(\tilde{\chi}^{0}_{1})$, and on scenarios with gravitino as the lightest
supersymmetric particle. Upper limits at the 95% confidence-level are set on
the higgsino production cross-section. Higgsino masses below 380 GeV are
excluded for the case of the higgsino fully decaying into a Higgs boson and a
gravitino.
