@beecee The rabbit hole of what underlies something understood as fundamental. If spacetime is emergent then it is emergent from something more fundamental, which would need a whole new set of theories for whatever spacetime emerges from.
True, the speed of light as a constant still holds to this day with no need for a physical medium. Yes, General Relativity is very successful, but the problem is with linking Quantum Mechanics and General Relativity, and gravity. Gravity is not treated with the SM of Particle Physics as there is no QFT for gravity. What little I know of LQG, space and time are quantized, probably also emergent from something more fundamental. In string theory, spacetime is likely to be emergent also.
It is, but string theorists, LQG theorists and other physicists have the idea that space and time is emergent from something more fundamental than space and time. Nima Arkani-Hamed is vocal about it for example.