A few points:
Light isn’t a wave. Light isn’t a particle. Light is something described by quantum mechanics that at times has the properties of both waves and particles, but is neither. As such light doesn’t require a medium.
In the Quantum Field Theory formulation of things, light is an excitation of the electromagnetic field, propagating through space. The EM field permeates all of spacetime.
Space is mostly empty of matter, but it’s still full of fields, the quantum vacuum, and spacetime itself. For example gravitational waves are disturbances in spacetime that propagate as waves.
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