With a load, without a load, or with the differential probe terminals shorted to each other and not even connected to the supply, the result looks the same. I think this is EM radiation from the supply rather than noise on the terminals. In fact this radiated noise is so large I can't even begin to measure what's actually on the terminals. If the probe terminals are connected to ground the result is even worse. In that case there is an additional sinusoidal component at the same frequency, 100kHz. This is with a custom built probe based on the AD8421.