"Quantum speed limit" as is usually used in the field has little to nothing to do with the speed of light. "Finite speed at which information propagates through space or time" appears also in theories that do not know about relativity or about space and time being unified. E.g. the "quantum speed limit" that has more to do with differential equations and control theory (the "boring" engineering field). Otherwise you are right, but the term you used will regretfully cause much confusion if people start googling its usual meaning https://en.wikipedia.org/wiki/Quantum_speed_limit