Hmmmm.
I thought they’d decided that photos can have mass in some circumstances.
I might be distorting a faint memory.
I recall hearing of experiments in which light was made to slow down by a factor of 10 or more.
Since energy and mass can be converted, one to the other, the energy in a photon does have an equivalent rest mass. But while it's a photon, it is purely energy, with no REST mass.
Photons entering and leaving a system or particles that do have rest mass (electrons, protons, neutrons, atoms, molecules), represents the conversion of energy to mass, and mass to energy. The mass of the system of particles that emits or absorbs a photon changes, the photon adds or subtracts mass by adding or subtracting energy.
The neutrino is a particle that is massless in some theories of physics, but most theories and some experiments indicate neutrinos have some (small) mass.