First, we have extensive observational data from elsewhere in the universe that tells us that the fundamental interactions work the same everywhere. For example, we see light coming from regions that have very different gravity, but it still behaves the same.

Second, on the scale of atoms, or even on the scale of ordinary macroscopic objects, gravity is so extremely weak that its effects on things like chemical bonds or the structure of nuclei, atoms, and molecules is negligible. If you have a very massive object like a star (or a white dwarf or neutron star), then of course you have different states of matter possible (degenerate matter in stellar cores, white dwarfs, and neutron stars), but even those states of matter still have all the fundamental interactions working the same way. The different states of matter are due to the extreme density and pressure, not due to any change in the fundamental interactions.

Third, what we usually call "the speed of light in vacuum" is actually a property of spacetime, not specifically of light. So the idea of this speed being "slowed down by gravity" is based on a confusion. That property of spacetime (a better name for it would be local Lorentz invariance) is the same everywhere no matter how weak or strong gravity is.