Everything Every Band All at Once I: A Global Morphology Catalog in Abell 2744 based on UNCOVER/MegaScience

We present spectrally-resolved structural parameter measurements of 28,274 sources from the legacy lensing field of Abell 2744, quantifying global structures from observed $0.7 \mu m - 4.8 \mu m$ and spanning rest-frame UV to NIR at $R\sim15$. These measurements are made on imaging mosaics mainly from the UNCOVER/MegaScience survey, including 20 JWST NIRCam broad and medium bands. We perform single-component S\'ersic fitting to these galaxies using \texttt{pysersic}, a Bayesian structural fitting tool, to infer their structural parameters and associated random uncertainties from the posterior distributions. Through various quality evaluation criteria, we infer robust structural parameters among $> 85\%$ of the selected $\rm SNR>10$ sources. For each galaxy with reliable sizes in at least two bands and a high quality redshift, we fit its observed size as a function of wavelength and infer rest-frame UV, optical, and near-infrared sizes where applicable. By performing injection-recovery tests on simulated galaxy cutouts in selected bands, we establish that our structural parameter measurements achieve fractional error $< 10 -20\%$ above $\rm SNR>10$. With this paper, all raw structural measurements and fitted rest-frame sizes are quality-flagged, cataloged, and released to the community. Finally, we demonstrate that this catalog enables the structural study of galaxies over an unprecedentedly wide parameter space of redshift ($0.3<z<8$), stellar mass ($\rm 10^{7}\, M_{\odot}<M_{*} <10^{11.5}\, M_{\odot}$), and rest-frame optical size ($\rm 100 \,pc<R_{e}<10\,kpc$), after correcting for lensing magnification.