You are correct; Shoho is our first victim as an IJN flattop, and Shoho was only a light carrier, not a fleet carrier. The IJN light carrier were considered little better than escorts for invasion fleets, and only out of necessity were put into the battle fleets in late 1942 after Midway.
But for their better speed, the IJN CL’s were more analagous to our escort carriers.
As for the “Yawata class” I would venture that by now, we have sunk all of the ones the Japanese built.
I’m actually even a bit unclear on what the Yawata class carrier is to be perfectly honest.
Near as I can tell they might be the Taiyo class escort aircraft carriers since the Unyo was a Taiyo class that was converted from the merchant Yawata Maru. That would place the class in which they are reporting on at three carriers that they have claimed two being sunk.
In reality the Unyo will not be sunk until September of 1944 when it is attacked by the submarine USS Barb. The other two will also go down in 1943 or 1944.
Maybe someone with a little more insight on naval matters knows more about this Yawata class.