Metal submerged in water without oxygen rust very very slowly. Then need to be exposed to air and also be wet to rust quickly.
Most hooks wear a hole in the fish and fall out during feeding or other activity.
I have caught many makos and billfish with hooks in their mouths that are worn and rusty, but all had lots of "meat" left and would not be rusting out soon.
None of the fish with single hooks in them seemed to have significant problems unless the area around the hook got infected to a large degree.
I suspect that circle hooks would stay in the fish's jaw longer than J hooks because of the small space between the barb and the shank, but because it is in the jaw, it will not do much damage to the overall health of the fish.