Okay, plug the washing machine into a receptacle on the laundry circuit and put the sewer alarm on the other circuit.
Here's my thought. There a space in the room that has the washer water connections and waste connection with a receptacle in that space for the laundry. This is fed by a 20 amp laundry circuit as required. Can I plug in a permanently installed/fastened in place sewer alarm into that receptacle or is another receptacle on a different circuit required?