Intervening metal absorbers in quasar spectra at z > 6 can be used as probes to study the chemical enrichment of the Universe during the Epoch of Reionization. This work presents the comoving line densities (dn/dX) of low-ionization absorbers, namely, Mg ii (2796 Å), C ii (1334 Å), and O  i (1302 Å) across 2 < z < 6 using the E-XQR-30 metal absorber catalogue prepared from 42 XSHOOTER quasar spectra at 5.8 < z < 6.6. Here, we analyse 280 Mg ii (1.9 < z < 6.4), 22 C ii (5.2 < z < 6.4), and 10 O i (5.3 < z < 6.4) intervening absorbers, thereby building up on previous studies with improved sensitivity of 50 per cent completeness at an equivalent width of W > 0.03 Å. For the first time, we present the comoving line densities of 131 weak (W < 0.3 Å) intervening Mg ii absorbers at 1.9 < z < 6.4 which exhibit constant evolution with redshift similar to medium (0.3 < W < 1.0 Å) absorbers. However, the cosmic mass density of Mg ii – dominated by strong Mg ii systems – traces the evolution of global star formation history from redshift 1.9 to 5.5. E-XQR-30 also increases the absorption path-length by a factor of 50 per cent for C ii and O i whose line densities show a rising trend towards z > 5, in agreement with previous works. In the context of a decline in the metal enrichment of the Universe at z > 5, the overall evolution in the incidence rates of absorption systems can be explained by a weak – possibly soft fluctuating – ultraviolet background. Our results, thereby, provide evidence for a late reionization continuing to occur in metal-enriched and therefore, biased regions in the Universe.