OK, I found a github project that handles taking a picture on the Gear 360 (2016) and downloading it using what seems like standard the v1 OSC API. No secret API to be found.
Missing parts:
- Transmitting the GPS coordinates to the phone at regular intervals or right before taking each picture using the API so the phone can store them in the EXIF data. This can be done using camera.setOptions
- stitching. (Edit: Perhaps this is automatically done when accessing the camera in Streetview/OSC mode)
The Gear 360 is one of the most popular and most affordable 360° cameras out there right now so I think it may be worth the effort to implement stitching for it on the backend (if the stitching in the app is slower than the smallest interval the camera can handle).