There seems to be some confusion about the meaning of "within the habitable zone". From the paper (Introduction and Conclusions, respectively) [1]: The habitability conditions of Proxima b, which orbits within the HZ of the star, have been extensively studied (e.g. Barnes et al. 2017; Ribas et al. 2016; Turbet et al. 2016; Meadows & Barnes 2018). On the other hand, the candidate Proxima d orbits much closer to the st…
Good catch "With the small stellar radius, Proxima d ... equilibrium temperature may reach 360K," NB: Earth's is 255K. Venus 260K, Mars 215K. So this doesn't tell the whole story, but is probably quite hot.
So it has a hot side, a cold side, and an intermediate ring at the terminator.
Probably not very comfortable.