  It has been proposed that the distinct formation and evolution of exoplanets
and brown dwarfs may affect the chemical and isotopic content of their
atmospheres. Recent work has indeed shown differences in the $^{12}$C/$^{13}$C
isotope ratio, provisionally attributed to the top-down formation of brown
dwarfs and the core accretion pathway of super-Jupiters. The ESO SupJup Survey
aims to disentangle the formation pathways of isolated brown dwarfs and
planetary-mass companions using chemical and isotopic tracers. The survey uses
high-resolution spectroscopy with the recently upgraded VLT/CRIRES$^+$
spectrograph, covering a total of 49 targets. Here, we present the first
results: an atmospheric characterisation of DENIS J0255-4700, an isolated brown
dwarf near the L-T transition. We analyse its K-band spectrum using a retrieval
framework where the radiative transfer code petitRADTRANS is coupled to
PyMultiNest. Gaussian Processes are employed to model inter-pixel correlations
and we adopt an updated parameterisation of the PT-profile. Abundances of CO,
H$_2$O, CH$_4$, and NH$_3$ are retrieved for this fast-rotating L-dwarf. The
ExoMol H$_2$O line list provides a significantly better fit than that of
HITEMP. A free-chemistry retrieval is strongly favoured over equilibrium
chemistry, caused by an under-abundance of CH$_4$. The free-chemistry retrieval
constrains a super-solar C/O-ratio of $\sim0.68$ and a solar metallicity. We
find tentative evidence ($\sim3\sigma$) for the presence of $^{13}$CO, with a
constraint on the isotope ratio of $\mathrm{^{12}C/^{13}C}=184^{+61}_{-40}$ and
a lower limit of $\gtrsim97$, suggesting a depletion of $^{13}$C compared to
the interstellar medium ($\sim68$). High-resolution, high signal-to-noise
K-band spectra provide an excellent means to constrain the chemistry and
isotopic content of sub-stellar objects, as is the main objective of the ESO
SupJup Survey.
