One of the surprising early findings with has been the discovery of a strong ``roll-over'' or a softening of the absorption edge of in a large number of galaxies at \(z 6\), in addition to systematic offsets from photometric redshift estimates and fundamental galaxy scaling relations. This has been interpreted as strong cumulative damped absorption (DLA) wings from high column densities of neutral atomic hydrogen ( signifying major gas accretion events in the formation of these galaxies. To explore this new phenomenon systematically, we assembled the PRImordial gas Mass AssembLy (PRIMAL) legacy survey of 584 galaxies at $z=5.0-13.4$, designed to study the physical properties and gas in and around galaxies during the reionization epoch. We characterized this benchmark sample in full and spectroscopically derived the galaxy redshifts, metallicities, star formation rates, and ultraviolet (UV) slopes. We defined a new diagnostic, the damping parameter to measure and quantify the net effect of emission strength, the fraction in the intergalactic medium, or the local column density for each source. The survey is based on the spectroscopic DAWN Archive (DJA-Spec). We describe DJA-Spec in this paper, detailing the reduction methods, the post-processing steps, and basic analysis tools. All the software, reduced spectra, and spectroscopically derived quantities and catalogs are made publicly available in dedicated repositories. We find that the fraction of galaxies showing strong integrated DLAs with $N_ HI $ only increases slightly from $ 60<!PCT!>$ at $z 6$ up to $ 65-90<!PCT!>$ at $z>8$. Similarly, the prevalence and prominence of emission is found to increase with decreasing redshift, in qualitative agreement with previous observational results. Strong emitters (LAEs) are predominantly found to be associated with low-metallicity and UV faint galaxies. By contrast, strong DLAs are observed in galaxies with a variety of intrinsic physical properties, but predominantly at high redshifts and low metallicities. Our results indicate that strong DLAs likely reflect a particular early assembly phase of reionization-era galaxies, at which point they are largely dominated by pristine gas accretion. At $z=8-10$, this gas gradually cools and forms into stars that ionize their local surroundings, forming large ionized bubbles and producing strong observed emission at $z<8$.