  The era of the James Webb Space Telescope ushers stellar population models
into uncharted territories, particularly at the high-redshift frontier. In a
companion paper, we apply the \texttt{Prospector} Bayesian framework to jointly
infer galaxy redshifts and stellar population properties from broad-band
photometry as part of the UNCOVER survey. Here we present a comprehensive error
budget in spectral energy distribution (SED) modeling. Using a sample selected
to have photometric redshifts higher than 9, we quantify the systematic shifts
stemming from various model choices in inferred stellar mass, star formation
rate (SFR), and age. These choices encompass different timescales for changes
in the star formation history (SFH), non-universal stellar initial mass
functions (IMF), and the inclusion of variable nebular abundances, gas density
and ionizing photon budget. We find that the IMF exerts the strongest influence
on the inferred properties: the systematic uncertainties can be as much as 1
dex, 2--5 times larger than the formal reported uncertainties in mass and SFR;
and importantly, exceed the scatter seen when using different SED fitting
codes. Although the assumptions on the lower end of the IMF induce degeneracy,
our findings suggest that a common practice in the literature of assessing
uncertainties in SED-fitting processes by comparing multiple codes is
substantively underestimating the true systematic uncertainty. Highly
stochastic SFHs change the inferred SFH by much larger than the formal
uncertainties, and introduce $\sim 0.8$ dex systematics in SFR averaged over
short time scale and $\sim 0.3$ dex systematics in average age. Finally,
employing a flexible nebular emission model causes $\sim 0.2$ dex systematic
increase in mass and SFR, comparable to the formal uncertainty. This paper
constitutes an initial step toward a complete uncertainty estimate in SED
modeling.
