  In the third paper of this series aimed at developing the tools for analysing
resolved stellar populations using the cameras on board of the James Webb Space
Telescope (JWST), we present a detailed multi-band study of the 2 Gyr Galactic
open cluster NGC 2506. We employ public calibration data-sets collected in
multiple filters to: (i) derive improved effective Point Spread Functions
(ePSFs) for ten NIRCam filters; (ii) extract high-precision photometry and
astrometry for stars in the cluster, approaching the main-sequence (MS) lower
mass of ~0.1 Msun; and (iii) take advantage of the synergy between JWST and
Gaia DR3 to perform a comprehensive analysis of the cluster's global and local
properties. We derived a MS binary fraction of ~57.5 %, extending the Gaia
limit (~0.8 Msun) to lower masses (~0.4 Msun) with JWST. We conducted a study
on the mass functions (MFs) of NGC 2506, mapping the mass segregation with Gaia
data, and extending MFs to lower masses with the JWST field. We also combined
information on the derived MFs to infer an estimate of the cluster present-day
total mass. Lastly, we investigated the presence of white dwarfs (WDs) and
identified a strong candidate. However, to firmly establish its cluster
membership, as well as that of four other WD candidates and of the majority of
faint low-mass MS stars, further JWST equally deep observations will be
required. We make publicly available catalogues, atlases, and the improved
ePSFs.
