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Okay, so the problem consisted of the following points. Read my updates for details:
Calibration of the Kinect 2 (yes, it's a tedious process but it has to be done... so rather do it now instead of wasting hours on trying to get around it like me. It's definitely worth it!)
The frames of the keypoint extraction and the Kinect point cloud have to match, of course. Sounds obvious but it apparently isn't.