> But that's for at-rest inertia. Photons are only very rarely if ever "at rest".
Not just rarely; photons are never at rest, period. In circumstances where one might intuitively think they might change speed, instead they change frequency.
That includes that they do not change speed in materials with a different index of refraction than a vacuum, but in that case, they do seem to, so as a shorthand it's often said that the speed of light in e.g. glass is slower than in a vacuum, but that's really just a shorthand -- so that's a can of worms.
Anyway your second equation is the full version of your much more famous first equation precisely because we need the extra term for photons (or any other massless things).
Not just rarely; photons are never at rest, period. In circumstances where one might intuitively think they might change speed, instead they change frequency.
That includes that they do not change speed in materials with a different index of refraction than a vacuum, but in that case, they do seem to, so as a shorthand it's often said that the speed of light in e.g. glass is slower than in a vacuum, but that's really just a shorthand -- so that's a can of worms.
Anyway your second equation is the full version of your much more famous first equation precisely because we need the extra term for photons (or any other massless things).