The special effect when the deathstar 1 hits Jedha in Rogue One and it has this ripple and explosion out into space and it takes a bit of time. I can imagine it looking something like this.
https://www.youtube.com/watch?v=Z79nF8m49FA

Granted the immediacy of the explosion in Episode 4 works in the movie’s pacing. It goes from about to fire on the rebel base and everything is great to particulate covering a massive amount of space.
https://www.youtube.com/watch?v=OyAohfiMsF4

And in RotJ it blows up in much of the same way but improved effects over Episode 4.
https://www.youtube.com/watch?v=XB1DdtdUAG0

Still though with special effects as they are today, neither of these explosions would have looked as they did back then today. “Devastating” the deathstar 1 in Episode 4 and having the Empire rebuild it seems a logical thing rather than starting from scratch, fixing all the weaknesses that Galen Erso built into the design.

Also, even in Episode 2 which takes place many years prior to Episode 4, they have the deathstar 1 plans.
https://www.youtube.com/watch?v=7ZpZzGOjRrc

And in Episode 3 you see the thing being built.
https://www.youtube.com/watch?v=DCoZItw93sQ

The point is that this took many years to design and construct, it is only completed during Rogue One which is immediately before the start of Episode 4. When did they start the deathstar 2? How did they get it online so quickly? In my mind it really makes sense to have the deathstar 1 being rebuilt as the deathstar 2 considering the time investment involved in the design and construction of it.