I don’t think there’s any question that the Death Star has hyperspace capabilities.
It was not something shown or stated in ANH. I don’t think it was meant to be an issue either way. That was something truly not important to the movie.
Anyway, I’ve explained what I think are some pretty obvious differences in the two situations.
I don’t think you have.
Disagreement is one thing but don’t deny obvious differences I’ve stated above.
To recap, assuming DS does hyperspace:
(1) ANH-only 30 minutes; TLJ-unknown amount of time, at least many hours
(2) ANH-DS jumps must take enormous energy; not as big a deal for normal ships