As for API documentation vs Library documentation it just seems like HotDoc is for Library documentation. (Even though it's the tastiest API documentation system) From their examples they are just showing Library documentation sites?
Docsgen is inspired by API docs like DO and PayPal where you have text on left and example request and response on the right. Example: https://developers.digitalocean.com/documentation/v2/
I have trouble finding examples of API documentation sites that uses HotDoc, feel free to link some and i will check them.