Why didn’t the Death Star just jump in a position where it could immediately fire at Yavin 4, instead of circling the planet for half an hour?
I never thought of the Death Star having hyperspace capability. As we try to rationalize travel times in a sciencey way that probably isn’t very realistic. But such is the burden of trying to make space fantasy = science. But let’s follow that thread. I think it very likely that in calculating the hyperspace jump, they didn’t account for the location of the orbit. Some slight additional travel time might be expected (in the movie, half an hour) to adjust, but that’s no big deal. Any jump with something the size of the Death Star would presumably expend a tremendous amount of energy. Just makes sense to finish the last 30 minutes of the journey in normal space.
Getting back to TLJ situation: the chase could go on for another day or longer. I don’t recall if the FO somehow knew exactly how much fuel they had. We know that the ships in question, in the movie, absolutely do have hyperspace capability. That should answer how the two situations are different.