c is the conversion factor between space (distance) and time, where 3 x 10^8 metres of distance is equal to 1 second of time.
c is also the maximum speed at which information can travel without causality problems. That means than all observers must agree on the sequence of events. There would be a big inconsistency if I pull the trigger of a gun, and the bullet strikes a target; and an observer somewhere, travelling at whatever speed, "measured the bullet to hit the target before I pulled the trigger". This is equivalent to "c is the conversion factor between space and time" and "Information cannot travel faster than c".
As light photons do not have mass, light travels at c(light) = c.
So, Special Relativity has nothing to do with the speed of light. Modern derivations of SR do not use the speed of light to derive the SR equations.
It just so happens that the speed of light is the same value as the c in SR, and that Einstein derived SR in terms of the speed of light.
If we discovered (we won't, but bear with me) that photons have a tiny mass, light would now travel at very slightly less than c. We would have to invent a new symbol, c(light), for the speed of light. But the c in SR (E = mc^2, Lorentz, etc) would remain c as today. SR would not use the speed of light, c(light).
It is no surprise that all inertial observers measure c to have the same value as c is a property of space-time.
From Maxwell's Equations, c = the reciprocal of (the square root of (the product of the permittivity, ε0 and the permeability, μ0 of space)). Permittivity is a measure of the electrical properties of space (vacuum) and permeability is a measure of the magnetic properties of space (vacuum).
Observers moving relative to each other measure different values for the distance between two events and different values for the times between those two events, but they always measure the same value for the Interval between those two events. The different distances and times they measure are related because 3 x 10^8 metres of distance is equal to 1 second of time.