It’s interesting that from the star’s perspective the light is immediately hitting the objects, yes those objects might have 200 million years of random chance and (possibly) free will determining their positions when the light hits

Not to mention that I'm not sure if all photons are guaranteed to hit anything. I have no intuition for calculating how likely that is for things in our neighborhood, but if you think of the star that is closest to the edge of the universe (as in, the farthest light could have traveled from the Big Bang, taking into account expansion of space itself), it seems unlikely that there would be guaranteed to be a chunk of matter between it and the universe's edge in every direction.

So a photon emitted in such a direction takes no time (from the photon's point of view) to be absorbed by its destination... only it has no destination and never will. It gives "what if a tree falls in a forest with no one to hear it?" vibes. Does the universe sort of "lose" the energy of that photon in a way that it doesn't for photons that are absorbed? Is it like The Great Memory Leak of the Universe or something? Is our existence leaking out between the fingers of the hand of God?

When you're moving at light speed there is no past or future. Everything is compressed into "now." I'm not sure how "random chance" works in such a situation, it's certainly not intuitive at least to me.