The principle of relativity suggests that all inertial frames are indistinguishable. But if I consider the rest frame of a photon (i.e. an IRF traveling at speed $c$ w.r.t. me), then won't it be distinguishable from my rest frame? And both are IRFs.

For example, time is not well-defined for the photon rest frame. I've heard that time stands still for a photon.

Isn't that a special property of photon rest frames, and therefore something that can be used to fundamentally distinguish it from regular IRFs (like mine)?