"Watt hour of storage" is not a unit, it's the physical quantity "storage" quantified by the unit "Watt hour", ie the combination of the two.
Wikipedia writes: “Storage capacity is the amount of energy extracted from an energy storage device or system; usually measured in joules or kilowatt-hours and their multiples”
https://world-nuclear.org/information-library/current-and-fu... writes: “Storage systems for electricity include battery, flywheel, compressed air, and pumped hydro storage. Any systems are limited in the total amount of energy they can store. Their energy capacity is expressed in megawatt-hours (MWh), and the power, or maximum output at a given time, is expressed in megawatts of electric power (MW or MWe).”
Both of which to my layman reading opposes your claim.