Blastophaga is more common than we think, but i don't think that it is, look different.
You should open a syconium, if you see the galls, or rather tiny insects, without a long "tail", you can be sure that it is Blastophaga.
I picked some caprifigs and there were more non pollinating wasps than blastophagas, in others lots of blastophagas, and in still others there was nothing...
The white edible can be a Dottato or Kadota.