Sure, but is the star dead from your view in the lab?
Let me put it another way, because I think there’s a degree of talking past each other going on:
The classic relativity example, the one where most of us hear of multiple reference frames for the first time, is the one with two astronauts, Anne and Bob, moving apart.
Anne looks out of her telescope (which is so powerful it can see Bob’s clock), and she sees Bob’s clock appears to both be behind her clock, and also ticking more slowly than hers (IIRC).
Now, in this scenario, we don’t try to work out what time it “really” is as there is no “really”. Likewise we don’t try to extrapolate backwards and say how long the light beam spent travelling because even that is problematic (how long the light beam spent travelling according to whom)?
We just simply say, in Anne’s reference frame, Bob’s clock says X.
Then we come to the example with the supernova, and ISTM we’re doing something quite different. We’re saying that from the POV of year 2000 astronomer, it only looked like the far away star’s clock was reading X. We can extrapolate backwards and apparently say that really the star’s clock was at time Y where Y is past the point it went nova.
This different treatment is what is making me uncomfortable.
I can see why in a practical sense we might choose to interpret events this way…in cosmology of course we are broadly looking “back in time” by looking further out, even if there is no universal “now”.
But that seems different to me than making a specific claim about reality of a specific event in the earth’s reference frame.