A comprehensive infrared spectroscopic study of star TRAPPIST-1 is a crucial step toward the detailed examination of its planets. While the presence of Earth’s atmosphere has limited the spectral extent of such a study up to now, the Near Infrared Imager and Slitless Spectrograph (NIRISS) and the Near Infrared Spectrograph instruments aboard the James Webb Space Telescope (JWST) can now yield the 0.6–5 μm spectral energy distribution (SED) of the star. Here we translate TRAPPIST-1's SED into tight constraints on its luminosity (L bol = 0.000566 ± 0.000022 L ⊙), effective temperature (T eff = 2569 ± 28 K), and metallicity ([Fe/H] = 0.052 ± 0.073) and investigate the behavior of its gravity-sensitive indices. Through band-by-band comparisons of the NIRISS and ground-based spectra, TRAPPIST-1 exhibits a blend of both field source and intermediate-gravity spectral characteristics, suggesting that the star is likely a field-age source with spectral features reminiscent of young objects. We also employ photospheric modeling incorporating theoretical and JWST spectra to constrain stellar surface heterogeneities, finding that the limited fidelity of current stellar spectral models precludes definitive constraints on the physical parameters of the distinct spectral components giving rise to TRAPPIST-1's photospheric heterogeneity and variability. In addition, we find intermodel differences in the inferences of properties (e.g., the effective temperature) over one order of magnitude larger than the instrument-driven uncertainties (∼100 K vs. ∼4 K), pointing toward a model-driven accuracy wall. Our findings call for a new generation of stellar models to support the optimal mining of JWST data and further constraining stellar—and ultimately planetary—properties.