What are the two components of this waveform generated by a MS-15 hall effect current sensor?
+/-0.5 voltage resembles a diode drop, of a diode bridge with no load except small capacitance in parallel with the output of the voltage gain of your CCVS =0.1 or an opto-coupled photo diode IC with a pull-up resistor on output that has very little LED current so not quite saturating .  Optocoupler diodes have an hFE of 0.1 typ.  Optocoupled transistors have a gain of 1 typ. but greater variation. These parts usually have 3-5kV isolation.

Most likely one of these parts.

It looks like your gnd reference is after the full Si diode bridge with 0.5V drop and no current .