Gas-phase metallicity as a function of H I column density. Filled red squares represent the GRBs from this work with positive H₂ detections, orange squares denote C I-bearing GRBs (where H₂ could not be constrained) from this work or Heintz et al. (2019a) and the green diamond symbols show the statistical GRB-DLA sample from Bolmer et al. (2019) without H₂ detections. For comparison, the large blue dots show the same ES-DLAs as shown in Fig. 10. The gray-shaded region and overplotted dashed lines show the expected increase in A_V for a given dust-to-metals ratio, in addition to the estimated detection probability f_det of dusty H₂-bearing GRB absorbers (see Sect. 5.2 for further details).