I noticed that in pymatgen.analysis.defects.corrections, the band edge shifting correction class takes both the hybrid VBM and CBM as arguments, but the actual correction only references the shift in the VBM at the hybrid functional level (line 859). I think this correction just accounts for the shift in the Fermi level for hybrid functionals, as referenced in section 1.1 of this paper https://arxiv.org/pdf/1904.11572.pdf . But for positively charged defects, wouldn’t we care about the CBM shift instead, since the electron is donated there? I would appreciate any insight if someone here knows why only the VBM shift is taken into account.
In the formalism for defining formation energy of an isolated point defect (see https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.86.253) used here, the energetic cost of changing the number of electrons in a defect calculation wrt bulk is taken into account by using Fermi level (VBM for 0K bulk) as a chemical potential for electron. For both positive/negative defects, which will involve removing/adding electrons from the same reservoir, only VBM shift affects the fermi level. So only that is used in calculating formation energy wrt bulk.
The paper you referenced, I believe tackles a different problem of shifting defect levels with the band edge shifts by calculating the projection on band edge states.