  Determining the clumpiness of matter around galaxies is pivotal to a full
understanding of the spatially inhomogeneous, multi-phase gas in the
circumgalactic medium (CGM). We combine high spatially resolved 3D observations
with hydrodynamical cosmological simulations to measure the cold circumgalactic
gas clumpiness. We present new adaptive-optics-assisted VLT/MUSE observations
of a quadruply lensed quasar, targeting the CGM of 2 foreground $z\sim$1
galaxies observed in absorption. We additionally use zoom-in FOGGIE simulations
with exquisite resolution ($\sim$0.1 kpc scales) in the CGM of galaxies to
compute the physical properties of cold gas traced by Mg\,II absorbers. By
contrasting these mock-observables with the VLT/MUSE observations, we find a
large spread of fractional variations of Mg\,II equivalent widths with physical
separation, both in observations and simulations. The simulations indicate a
dependence of the Mg\,II coherence length on the underlying gas morphology
(filaments vs clumps). The $z_{\rm abs}$=1.168 Mg\,II system shows coherence
over $\gtrsim$ 6 kpc and is associated with an [O\,II] emitting galaxy situated
89 kpc away, with SFR $\geq$ 4.6 $\pm$ {1.5} $\rm M_{\odot}$/yr and
$M_{*}=10^{9.6\pm0.2} M_{\odot}$. Based on this combined analysis, we determine
that the absorber is consistent with being an inflowing filament. The $z_{\rm
abs}$=1.393 Mg\,II system traces dense CGM gas clumps varying in strength over
$\lesssim$ 2 kpc physical scales. Our findings suggest that this absorber is
likely related to an outflowing clump. Our joint approach combining
3D-spectroscopy observations of lensed systems and simulations with extreme
resolution in the CGM put new constraints on the clumpiness of cold CGM gas, a
key diagnostic of the baryon cycle.
