From a philosophical point of view, an event happens at the point when observed by an observer.
For us, Humans on earth, this supernova happens now and not 120 million years ago.
If a tree falls in a forest and we stumbled upon it today, I don’t think philosophy says that the tree fell today. I think it says we found a fallen tree today.
The supernova didn’t happen today, we found evidence of it today.
Minkowski spacetime confuses matters, though. From the point of view of the photon we observe, no time elapses between its emission at the location being observed and its arrival at the telescope image sensor. It's as if the photon were born in exactly the right place and time to be observed by us, at that very instant.
So what we see is arguably happening in real time, regardless of distance.
Ehh. The measurement is happening in real time but we have well-defined ways to say when the event happened, and that's 120MY ago (given the reference frame where Earth is motionless).
Depends on what you mean by "real time". If by "real time" you mean "the spacetime interval between the event 'supernova explodes' and 'explosion observed on earth' is lightlike (or null)", then we witnessed it in real time. I can't think of any other definition that is observer independent.
I also argue that it is not well-defined, as the time span depends on the observer, as you say. Did it happen 120MY ago or 1MY ago? Both can be true for different observers, and none is privileged over the other.
I think even philosophy can withstand knowing the speed of light and incorporating it into the framework of 'when things happened' so that it agrees with our understanding of the universe instead of not.
Say you were immortal and witnessed a supernova from a million light-years away. Eventually, after another million years have passed, you meet another immortal who happened to be right next to the supernova when it happened. When talking to this other immortal, would you refer to the event as happening two million years ago (when you witnessed it), or three million years ago (when the other immortal witnessed it)?
If a tree falls in a forest and we stumbled upon it today, I don’t think philosophy says that the tree fell today. I think it says we found a fallen tree today.
The supernova didn’t happen today, we found evidence of it today.