Understanding how galaxies assemble their structure and evolve morphologically over cosmic time is a central goal of galaxy evolution studies. In particular, the morphological evolution of quiescent and star-forming galaxies provides key insights into the mechanisms that regulate star formation and quenching. We present a new catalog of morphological measurements for more than 340000 sources spanning 0<z<12, derived from deep JWST NIRCam imaging across four major extragalactic fields (CEERS, PRIMER-UDS, PRIMER-COSMOS, GOODS) compiled in the DAWN JWST Archive (DJA). We performed two-dimensional surface brightness fitting for all galaxies in a uniform, flux-limited sample. Each galaxy was modeled with both a Sersic profile and a two-component (bulge and disk) decomposition, yielding consistent structural parameters, including effective radius, Sersic index (n_S_, axis ratio, and bulge-to-total ratio (B/T). To demonstrate the scientific application of our morphology catalogs, we combined these measurements with DJA photometric redshifts, physical parameters and rest-frame colors, and investigated the relation between total, bulge, and disk sizes, n_S_, star formation activity, and redshift. Bulge-dominated galaxies (high n_S_ and B/T) predominantly occupy the quiescent region of the UVJ diagram, while disk-dominated galaxies are mostly star-forming. A significant bimodality persists, with quiescent disks and compact, bulge-dominated star-forming galaxies observed out to z>3. Quiescent galaxies also show significantly higher stellar mass surface densities, nearly an order of magnitude greater at z~4 than at z~1. Our results confirm a strong and evolving link between morphology and star formation activity and support a scenario in which bulge growth and quenching are closely connected. This work is a highly valuable addition to the DJA, adding a morphological dimension to this rich dataset and thus enabling a wider scientific application.