Cumulative soft X-ray and Lyman-Werner background intensities from PBHs accreting within halos under different model assumptions. Each column corresponds to a specific PBH mass (M_PBH = 1 M_⊙, 10 M_⊙, 33 M_⊙, and 100 M_⊙) and the f_PBH value derived from the baseline model where the observational (nsCXB) or theoretical (J_LW ∼ 1) thresholds are exceeded. The top row shows the soft X-ray background intensity (J_{0.5 − 2 keV}), while the bottom row displays the LW background intensity (J_LW). The coloured lines represent different model variations: baseline model (blue), Ziparo+2022 velocity (green), standard ADAF without subregimes (yellow), CDM power spectrum (red), and isothermal PBH distribution (purple). Dashed and dashed-dotted lines correspond to results using the simple isothermal and Makino+1998 density profiles, respectively. The grey shaded region in the top row indicates the observed excess X-ray background from Cappelluti et al. (2017), and the dashed grey line in the bottom row marks the critical J_LW ∼ 1, where molecular hydrogen dissociation balances its formation.