Since the medium in which light propagates is spacetime, would light be able to exist if spacetime did not exist? Is this like one of those chicken/egg problems, or can light be thought of as a legitimately independent entity? This might be bordering on an philosophical question, so if it is, let me know and I'll delete it.
Space-time is not really a "medium", it does not vibrate when a light wave is passing through. It just gives a reference of positions and instants in times in order to measure these quantities. Waves always need variations in time and space so you need to define the space-time first.
The "oscillating thing" of light waves is called the "electromagnetic field", which is not composed of matter per se. We do not perceive it directly. We are only able to observe some of its consequences, for example the light that gets in our eye, or the heat that we feel from the sun.
A couple related questions:
Light cannot exist without spacetime.
Every light ray has one place of emission and one place of absorption. You might agree that between both places there must be a spatial distance, otherwise there would be no light ray and no transport of momentum.
Light in vacuum (v=c) is associating this spatial interval with a zero spacetime interval, because it is a lightlike movement. This seems to be an essential characteristic of light so that I would say that the concept of light is closely linked to the concept of spacetime, and it cannot exist without spacetime. Philosophical considerations are not required.