Drywall around kitchen sink

While I love my apartment, clearly the landlord did some things on the cheap, including not tiling around the kitchen sink. A few years in, the drywall to the left of the sink has started to disintegrate and peel. This is a rental, so I don’t want to do too much, but the hole is unsightly and bothers the crap out of me.

I’m assuming it’s too big to just stick caulk over - would it be something I should use joint compound on? I’m planning on recaulking the seam afterwards, but obviously would love to fix the hole first. And if there is any advice on a longer term solution (quarter round silicone trim maybe?), I love to hear any thoughts.

Thanks in advance!