PN 16010-333-004 is a crb gasket set. The genuine Honda set includes all gaskets to service one carb, not the entire rack of four.
The brass parts are under different PNs from Honda, there is no OEM "carb kit complete" available. Partzilla appears to sell the real McCoy.
Aftermarket carb kits, line the one linked above, have non-OEM brass parts that have often caused tuning problems because they are not identical to the Keihin ones. These kits have some gaskets but usually not the fuel tube/tee O-rings. The bowl gasket O-rings in some of these kits swell a lot when exposed to gasoline.
I would buy four Honda seal kits and possibly float valves. Unless your bike has quite high mileage (not normal for a 400F... rather buzzy for transcontinental trips) the brass parts will be fine - a thorough cleaning is all they should need.