Drywall hairline cracks
If you did use drywall tape, then the cracks just need to be filled in with more drywall mud/joint compound. The mud probably contracted as it dried, and the sanding revealed a "cave" of sorts. Just re-mud. Do NOT use caulk. It has a different texture and will probably show up as a thin line in the final result.
You will need to re-prime those spots once the joint compound dries.