Pedantic note: The speed of light in glass, optical fiber and water is different from vacuum (much lower). On a certain scale, humanity also knows how to locally alter the speed of light though not to this extent.
You're conflating two very different meanings of "the speed of light". Confusingly, "speed of light" can refer to the universal constant, c, which does not change in glass, or to the speed that light travels in a medium. Here, we're talking about c. Relativistic effects are based only on c. The Three Body Problem trilogy plot device is also about c.
It's not actually that the speed of light in a singlemode fiber optic cable is slower, but that the photons aren't travelling in a direct path down the fiber like water down a pipe. They're bouncing off the interior walls of it at like a 45 degree angle billions/trillions of times before it reaches the other end of the cable.
Basically imagine like if you wanted to walk in a straight line between two points at both ends of a empty, long, narrow rectangular warehouse, and instead of walking in a straight line from A to B, you bounced off each wall at an angle (like a pool ball ricocheting off the bumpers) to get from one end to the other. Making your cumulative distance travelled on foot much greater.