Because the backlash occurs on the Y axis (and assuming hardware similar to my machine), it’s likely in the couplings between the motor and the jackshafts across the back of the machine:
You may have a more complex arrangement:
In any event, carefully examine all those joints to find the slightly loose setscrew. It may be jammed on one side of the shaft flat, so try to loosen each screw: the one that moves was the loose one.