It would really be the Earth staying still. If the sun stayed still relative to the galactic centre, we would still have daylight cycle on Earth, and probably wouldn’t notice that the sun’s orbit of the galactic centre had been paused by a few Earth hours.
Is this just attempting to one up … what is it, the book of Joshua, where the sun just stays still for 72 hours?
It would really be the Earth staying still. If the sun stayed still relative to the galactic centre, we would still have daylight cycle on Earth, and probably wouldn’t notice that the sun’s orbit of the galactic centre had been paused by a few Earth hours.