Well, they're not as advanced as DJ's SDK, but it works for my robot :). The one of iOS only has servo control as I started it this weekend. It requires jailbreaking though as Apple can only talk with their approved devices or BLE, and your bluetooth module is not BLE, sorry for that :P. Anyways here they are
The mac version uses MonoMac for GUI, but the underlying library is built on Mono so works on Windows and Linux too.
For iOS I don't use Xcode, I use theos make system and objective c, if you're willing to jailbreak check it out . To build you need to install BTStack library. If anyone wants Ill make a video of the steps sometime.
Just know, they're primitive, I'm not DJ :). But if anyone actually uses it and wants a feature I can add it :).