Yes, the listing was for "all accessories" and the battery is listed as included on the box. So they owe me a Sony battery or a big lump of money back.
Did you contact them straight away and ask “where’s the battery?” ? Normally I try give ebay people a tiny benefit of the doubt. Then if they’re a dick they can have the ‘not as described’ returns shitstorm.
I wouldn't bother with the proper Sony ones. Though you would have thought they would have supplied the battery with the camera?