The James Webb Space Telescope (JWST) provides low- to medium-resolution spectra with unprecedented precision and broad near- to mid-infrared wavelength coverage, thus enabling the detailed characterization of exoplanet atmospheres. Given the complexity of JWST data and the diversity of observing modes, it is essential to understand the information content of the resulting spectra to optimize observation strategies and assess the limits of atmospheric inference. This work presents a new JWST NIRISS SOSS transit observation of the warm sub-Saturn HAT-P-12b. Together with complementary NIRSpec G395M and MIRI LRS data, this enables a detailed assessment of the information content across JWST instruments over the full accessible wavelength range (excluding MIRI MRS). The NIRISS data were reduced, and the impact of specific reduction choices on the resulting transmission spectrum was assessed. Atmospheric retrievals were performed for all combinations of JWST data, supplemented by archival HST observations in select cases. The analysis further included evaluations of molecular detection significances and assumptions about the atmospheric structure. The same four molecules previously reported are significantly detected: H_2_O, CO_2_, CO, and H_2_S. Except for H_2_O, all require NIRSpec coverage for detection, while H_2_S is only detected in multi-instrument retrievals. Abundance constraints obtained using HST WFC3 instead of JWST NIRISS SOSS are largely consistent, particularly when combining instruments, but NIRISS SOSS proved essential to establishing robust evidence for nongray cloud behavior. A moderately steep scattering slope (p<4) is consistently retrieved across different HST STIS reductions. Single-instrument retrievals, even when yielding significant detections, tend to overestimate molecular abundances. In contrast, retrievals that combine spectra from multiple JWST instruments generally converge toward consistent abundance constraints. The derived C/O ratio remains sensitive to subtle differences between NIRSpec reductions, owing to the instrument's exclusive coverage of the carbon-bearing molecules CO_2_ and CO, so its interpretation requires caution. The results are broadly consistent with information content studies of the benchmark target WASP-39b, although differences, including the absence of a preference for non-isothermal T-P profiles, highlight variations in information content across exoplanet types.