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Einstein was not talking about light in his SR and GR theories. He was talking about the "speed" of light. As simple as that is, took me a long time to get it.

Interesting thanks. I hadn’t seen it elsewhere myself but I could see how it’s taken off. OP’s article almost gets there, but never says that specifically. Rather it says “c is not a property of light, it’s a property of the universe.”

Landau & Lifshitz, in their (classic) book on The Classical Theory of Fields, begin with a section called "Velocity of propagation of interaction".