So in the context of a load-limiting breaker which makes or breaks the circuit that powers the load, how does that monitor it?
I don't know how any such devices do it. Although, as I have said, it would not be without its potential problems, one way would be to apply power to the load through a 'substantial' (in relation to that of the expected load) resistance and measure the resultant (modest/small) current.
As I've said, I would personally not have thought that it would be very desirable to repeatedly apply 'full power' to the circuit (without a resistor/whatever), even for less than one cycle, not the least because there might be a fault in the load (or circuit) resulting in a very low impedance - although stillp seems to have indicated that such is one way in which it is done.