  The SPT0311-58 system resides in a massive dark matter halo at z ~ 6.9. It
hosts two dusty galaxies (E and W) with a combined star formation rate of ~3500
Msun/yr. Its surrounding field exhibits an overdensity of sub-mm sources,
making it a candidate proto-cluster.
  We use spatially-resolved spectroscopy provided by the JWST/NIRSpec Integral
Field Unit (IFU) to probe a field of view (FoV) ~ 17 x 17 kpc^2 around this
object.
  These observations have revealed ten new galaxies at z ~ 6.9, characterised
by dynamical masses spanning from ~10^9 to 10^10 Msun and a range in radial
velocities of ~ 1500 km/s, in addition to the already known E and W galaxies.
The implied large number density, and the wide spread in velocities, indicate
that SPT0311-58 is at the core of a proto-cluster, immersed in a very massive
dark matter halo of ~ 5 x 10^12 Msun. Hence, it represents the most massive
proto-cluster ever found at the EoR. We also study the dynamical stage of the
system and find that it likely is not fully virialised.
  The galaxies exhibit a great diversity of properties showing a range of
evolutionary stages. We derive their ongoing Ha-based unobscured SFR, and find
that its contribution to the total SF varies significantly across the galaxies
in the system. Their ionization conditions range from those typical of field
galaxies at similar redshift recently studied with JWST to those found in more
evolved objects at lower z. The metallicity spans more than 0.8 dex across the
FoV, reaching nearly solar values in some cases. The detailed IFU spectroscopy
of the E galaxy reveals that it is actively assembling its stellar mass,
showing sub-kpc inhomogeneities, and a metallicity gradient that can be
explained by accretion of low metallicity gas from the IGM. The kinematic maps
indicate departures from regular rotation, high turbulence, and a possible
pre-collision minor merger. (Abridged)
