The IR bolometer does (more or less) count photons, and hence measures radiant power.
Sigh. I did cover the indirect measure, but .... it simply does not count photons. There is no photon counter in it. Rather, it measures absorbed energy, i.e., heat, through a temperature rise in the bolometer material, creating a resistance change, which has been calibrated. It is resistance which is actually measured, but this resistance change is a direct effect of temperature rise from absorbed power. One could, down the road, estimate the number of photons from the wavelength and total energy in the band, but .... that is not "counting" at all, but a theoretical calculation.