So the 7 mV was measured without any load. Just measuring over a single resistance I get these numbers from my ancient Fluke 79ii (voltage, resolution 1 mV) and Uni-T 61 (current):
All measurements with channel turned off.
8 kOhm, 7 mV, 1 muA (micro Amp)
1000 Ohm, 5 mV, 5 muA
100 Ohm, 2 mV, 12 muA
12 ohm, 1 mV, 13 muA
1 ohm, 0 mV, 10 muA
When the channel is set to ON, but output set to 0 V, for 100 Ohm, I measure 1 mV, 3 muA which is different from above when channel output is set OFF.
I probably shouldn't worry, but I just replaced a cheap Korad 3005 clone that had 70V spikes when hardpowering off even if soft power was already off. I have not checked this new supply for that kind of behaviour yet.