You should use either paper tape or fiberglass mesh tape in the joint between the boards, so use that and build up the damaged area with filler so it covers as much as possible. After that, use flexible filler in the joint as usual.
Corners cracking happens from time to time and it’s nothing to worry about, but as mentioned. Repair it with filler. Building something up with caulk doesn't look as nice and is often visible - filler, on the other hand, becomes as hard as gypsum.