I don't follow the comics either, and I'm sure there could be good reasons to the contrary, but I would just think that by the 31st century, he would be long dead of old age. I know Kryptonians gain super powers from our yellow sun, But I never got the impression that they were immortal, or even that their lifespan overly exceeded that of humans.
The recent conclusion to "Thy Kingdom Come" in Justice Society
shows what happens to Clark Kent/Superman in the Kingdom Come
timeline; he's still alive when the Legion is active, albeit very