  A search is performed for light, spin-0 bosons decaying into two photons in
the 66 to 110 GeV mass range, using 140 fb$^{-1}$ of proton$-$proton collisions
at $\sqrt{s}=13$ TeV produced by the Large Hadron Collider and collected by the
ATLAS detector. Multivariate analysis techniques are used to define event
categories that improve the sensitivity to new resonances beyond the Standard
Model. A model-independent search for a generic spin-0 particle and a
model-dependent search for an additional low-mass Higgs boson are performed in
the diphoton invariant mass spectrum. No significant excess is observed in
either search. Mass-dependent upper limits at the $95\%$ confidence level are
set in the model-independent scenario on the fiducial cross-section times
branching ratio into two photons in the range of 8 fb to 53 fb. Similarly, in
the model-dependent scenario upper limits are set on the total cross-section
times branching ratio into two photons as a function of the Higgs boson mass in
the range of 19 fb to 102 fb.
