Hi DanJust for my own clarity I'm not quite sure what you mean by "Einstein's photon" and QED's photon. Yes, Einstein had derived E = pc (v = c since we have a photon) and only used the energy and momentum properties, but what specifically do you mean by a QED photon?
Qouting from https://www.britannica.com/science/quantum-electrodynamics-physics#
QED rests on the idea that charged particles (e.g., electrons and positrons) interact by emitting and absorbing photons, the particles that transmit electromagnetic forces. These photons are “virtual”; that is, they cannot be seen or detected in any way because their existence violates the conservation of energy and momentum. The photon exchange is merely the “force” of the interaction, because interacting particles change their speed and direction of travel as they release or absorb the energy of a photon. Photons also can be emitted in a free state, in which case they may be observed as light or other forms of electromagnetic radiation.
My understanding at the moment is the Photons in the free state are the same as Einsteins photons. These are not the propagators of radio waves, they carry inertia and spin and have momentum they are particles in their own right. Radio waves are propagated by virtual photons which represent a wave, of electromagnetic energy.