  Measurements of differential cross sections are presented for inclusive
isolated-photon production in $pp$ collisions at a centre-of-mass energy of 13
TeV provided by the LHC and using 139 fb$^{-1}$ of data recorded by the ATLAS
experiment. The cross sections are measured as functions of the photon
transverse energy in different regions of photon pseudorapidity. The photons
are required to be isolated by means of a fixed-cone method with two different
cone radii. The dependence of the inclusive-photon production on the photon
isolation is investigated by measuring the fiducial cross sections as functions
of the isolation-cone radius and the ratios of the differential cross sections
with different radii in different regions of photon pseudorapidity. The results
presented in this paper constitute an improvement with respect to those
published by ATLAS earlier: the measurements are provided for different
isolation radii and with a more granular segmentation in photon pseudorapidity
that can be exploited in improving the determination of the proton parton
distribution functions. These improvements provide a more in-depth test of the
theoretical predictions. Next-to-leading-order QCD predictions from JETPHOX and
SHERPA and next-to-next-to-leading-order QCD predictions from NNLOJET are
compared to the measurements, using several parameterisations of the proton
parton distribution functions. The measured cross sections are well described
by the fixed-order QCD predictions within the experimental and theoretical
uncertainties in most of the investigated phase-space region.
