  We report new observations of the cool diffuse gas around 29, $2.3<z<6.3$
galaxies, using deep JWST/NIRCam slitless grism spectroscopy around the
sightline to the quasar J0100+2802. The galaxies span a stellar mass range of
$7.1 \leq \log M_{*}/M_{sun} \leq 10.7$, and star-formation rates of $-0.1 <
\log \; SFR/M_{sun}yr^{-1} \; <2.3$. We find galaxies for seven MgII absorption
systems within 300 kpc of the quasar sightline. The MgII radial absorption
profile falls off sharply with radii, with most of the absorption extending out
to 2-3$R_{200}$ of the host galaxies. Six out of seven MgII absorption systems
are detected around galaxies with $\log M_{*}/M_{sun} >$9. MgII absorption
kinematics are shifted from the systemic redshift of host galaxies with a
median absolute velocity of 135 km/s and standard deviation of 85 km/s. The
high kinematic offset and large radial separation ($R> 1.3 R_{200}$), suggest
that five out of the seven MgII absorption systems are gravitationally not
bound to the galaxies. In contrast, most cool circumgalactic media at $z<1$ are
gravitationally bound. The high incidence of unbound MgII gas in this work
suggests that towards the end of reionization, galaxy halos are in a state of
remarkable disequilibrium, and are highly efficient in enriching the
intergalactic medium. Two strongest MgII absorption systems are detected at
$z\sim$ 4.22 and 4.5, the former associated with a merging galaxy system and
the latter associated with three kinematically close galaxies. Both these
galaxies reside in local galaxy over-densities, indicating the presence of cool
MgII absorption in two "proto-groups" at $z>4$.
