Over the past decade, the open frame (``cagey'') structure of $\mathrm{CoS}{\mathrm{b}}_{3}$ skutterudite has invited intensive filling studies with various rare-earth elements for delivering state-of-the-art midtemperature thermoelectric performance. To rationalize previously reported experimental results and provide new insight into the underexplored roles of La fillers and Sb vacancies, ab initio density functional theory studies, along with semiclassical Boltzmann transport theory calculations, are performed for pristine $\mathrm{CoS}{\mathrm{b}}_{3}$ of different lattice settings and La-filled $\mathrm{CoS}{\mathrm{b}}_{3}$ with and without Sb's mono- and divacancy defects. The effects of spin-orbit coupling (SOC), partial La filling, Sb vacancy defects, and spin polarization on the electronic and thermoelectric properties are systematically examined. The SOC shows minor effects on the electronic and thermoelectric properties of $\mathrm{CoS}{\mathrm{b}}_{3}$. The peculiar quasi-Dirac band in the pristine $\mathrm{CoS}{\mathrm{b}}_{3}$ largely survives La filling but not Sb vacancies, which instead introduce dispersive bands in the band gap region. The non-spin-polarized and spin-polarized solutions of La-filled $\mathrm{CoS}{\mathrm{b}}_{3}$ are nearly degenerate. Importantly, the band structure, density of states, and Fermi surface of the latter are significantly spin polarized, giving rise to spin-dependent thermoelectric properties. Seebeck coefficients directly calculated as a function of chemical potential are interpreted in connection with the electronic structures. Temperature-dependent Seebeck coefficients derived for the experimentally studied materials agree well with available experimental data. Seebeck coefficients obtained as a function of charge carrier concentration corroborate the thermoelectrically favorable role at high filling fractions played by the Fermi electron pockets associated with the degenerate valleys in the conduction bands, and also point toward a similar role of the Fermi hole pockets associated with the degenerate hills in the valence bands. These results serve to advance the understanding of $\mathrm{CoS}{\mathrm{b}}_{3}$ skutterudite, a class of materials with important fundamental and application implications for thermoelectrics and spintronics.