to answer this question, ordinarily, i would just reach for the nearest sci-fi game and tell you how they implemented it, but the only game that comes to mind is Space Engineers and that game has both of these

The second one, but standing on the outside of the sphere. It rotates around the gun.

Probably A. It would likely have used artificial gravity just like any starship. Star-Trek has it built into the deck plates but I dunno how Star Wars does it. Artificial gravity can then be dialed in to compensate for the natural gravity of the structure. Which is probably less than you'd think. Without normal gravity effects, the internal air and water pressure will be mostly uniform across the ship instead of denser towards the core.

Same with the matter making up the structure. It'll largely be hollow and filled with air, so much lower natural gravity than an actual moon of the same size. According to official sources (referenced here: https://scifi.stackexchange.com/questions/92401/is-the-death-star-s-gravitational-force-strong-enough-to-hold-an-atmosphere) it's between 120 & 160 km radius, for a probable gravity of ~0.04g. That's not quite microgravity, but still far too low to be walking around in. For comparison Lunar gravity is ~0.166g.

It's not gravity, it's the Force^TM^

Besides technical diagrams from supplementary stuff, the Falcon lands in a docking bay that's oriented towards the first option. There could be some kind of transition point to the second option, but we don't see it and it'd be really awkward.