It’s complicated (and don’t trust me too much, I’m not qualified), but if you’ve heard of time dilation and whatnot, if you start traveling at speeds comparable to the speed of light, spacetime distorts in such a way that from your point of view all light coming from any direction travels at the same speed.

This is also why (or one of the reasons) according to science you cannot travel faster than the speed of light, since light would still need to be traveling away from you at the speed of light and you’d need to occupy negative space in that direction, or something like that.