So instead of a RTSP cam, I used the ONVIF binding thing and this at least makes the thing go offline when I reboot the camera.
Unfortunately, the process (ffmpeg audio detection) does not restart when the ONVIF camera comes back online so that will indeed be a rule I need to create I guess (changing threshold by just a bit).
When writing this, I also tried to simply disable the thing and re-enable it, I would expect that at least the audio detection should start on Openhab/Thing startup. That also does not happen but that might be pretty simple to fix in the binding right?