A 4 K dry cryostat’s refrigeration system usually eats about 4-5 kW. Not sure what’s going on here.
It is, IMO, a bit dubious whether or not anything is truly flowing in a superconductor at constant current. Electrons don't have identity, so the 'constant flow of electrons' can be rephrased as 'the physical system isn't changing'... and the degree to which you can tell that there are electrons moving about is also the degree to which the superconductor isn't truly zero-resistance.
Of course it isn't actually constant -- there are multiple electrons, and you can tell that the electron field is quantized. But the degree to which that is visible, is the exact degree to which the superconductor nevertheless doesn't superconduct!
You can't quote a number for the cryocooler without knowing how much heat is being injected into the thing it needs to keep below 4.2K.