There’s always been a lot of sadness in hip-hop. Though the term “sad rap” brings to mind “What’s Up Fatlip?” It’s self-mocking, so it’s not as overtly emo as the ones in the link.
“I make myself sick, get on my own nerves/Immature, insecure grown up nerd/Has-been MC on a label that’s unstable/Choppin’ bliggy on the table.”