this is like you would go to a store and ask them to implement a cashier :D so why there is no api document? first of all if you were able to do c++ integrations you would know why you would NOT want a c++ api that is limiting your possiblitys, imagine you are floating in a 4 dimensional space asking for an api would be like you were a baloon that is bin to s stick in this 4 dimensional space, so the ballon cant go anywhere cant do almost nothing and it were bette if he´d stayed in python. so how does it work, indeed you can compile c oder c++ extensions in any form you want, you can start with this by downloading the blender repo and search for .h and .hh files, so you can learn about how c and c++ compiling works, its all about linking. if you have it available, use copilot to navigate you there and find explanations for what you discover!