Well WorldMap wasnt so important for me anyway (Minimap otherwise is essential - but in fairplay mode - and no other alternative approaches in vanilla look and feel).
About 1.13.1 i think Forge will backport .1 bugfixes back to 1.13 builds for a while just like they did before (1.8 to 1.12).
It's one of those mods that extracts a component of itself into mods/1.12.2.
You'll need to remove this as well because the component gets loaded and assumes the rest of the mod is there, then crashes when it can't find it.
Instead of implementing ICapabilityProvider implement ICapabilitySerializable and in the methods deserialize and serialize call CapabilityItemHandler.ITEM_HANDLER_CAPABILITY.getStorage().readFromNBT and writeToNBT respectively.
ItemStack#copy() serializes the capability data and if it can't be serialized then it won't be transferred over.
Try use ICapabilitySerializable instead of ICapabilityProvider and use the Capabilities getStorage() function to deserialize and serialize the IItemHandler.