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I actually just asked a question on the physics stack exchange that is semi relevant to this. https://physics.stackexchange.com/questions/810429/functiona...

In my question I was asking about a hypothetical time-evolution operator that includes an analog of a light cone that you could think of as a context window. If you had a quantum state that was evolved through time by this operator then I think you could think of the speed of light being a byproduct of the width of the context window of some operator that progresses the quantum state forward by some time interval.

Note I am very much hobbyist-tier with physics so I could also be way off base and this could all be nonsense.