I already noticed i was wrong, and did clear my previous posting (can't delete postings). However in the mean time found the real reason:
ShipBlueprintDefs.xml: AssaultCarrierBlueprint specifies the EscortCarrierModule as type.
ComponentClassDefs.xml: Specifies EscortFightersCap for EscortCarrierModule as prime stat.
ShipComponentDefs.xml: For the EscortCarrierModule it raises AssaultFightersCap as the EffectType, and specifies AssaultCarrierModule as Type (as you already noticed).
Changing the EffectType in ShipComponentDefs.xml for the EscortCarrierModule to EscortFightersCap, on top of the change you already did (setting the Type to EscortCarrierModule) fixes it.