TLDR: I think Rogue One breaks not only lore, but the internal logic of the films.

So in the OT, the Death Star is fully complete in the first movie. The time between Ep4 and 6 is roughly 4-5 years. In that time the Death Star II is roughly 85-95% complete visually speaking. It’s also said to be about twice the size of the original. With that said let’s go back. Episode 2 shows the plans for the original Death Star to be built. Based on George Lucas’s director commentary, he says that the Geonosians build the station. Assuming they start at the beginning of the Clone Wars by the end of Ep3 they are about what looks to be 10-20% over the course of the 3 year war. Also assuming that because of the war, most resources were diverted away from the project towards funding both sides of the war. So that should mean that after the war more if not most resources would now be diverted back to the Death Star construction since all star systems would easily fall if not voluntarily under the empire and the imperial military would already be spread across the galaxy.

So in Rogue One, which would be around 20 years later, why would the Death Star be finally completed, taking 23 years. When the second, larger Death Star was nearly done in 4 years.