Agree, that was my main takeway too. I found the animation with the two mirror systems especially illuminating. Without the theory of spacetime, it would seem

Agree, that was my main takeway too. I found the animation with the two mirror systems especially illuminating. Without the theory of spacetime, it would seem that the two mirror systems would somehow get out of sync over time, since it appears, from the stationary system, as if the photons in the moving system are doing fewer rounds in the same amount of time. And from the moving system the photons in the stationary system appears, likewise, to be doing fewer rounds. The theory reconciles it by saying that time itself is not fixed, but dependent upon relative motion. And the relative motion is something that observers at both systems can agree upon. So, by accepting that time is dependent upon relative motion, they can agree upon the motion of photons in both systems.