Please accept our apologies for delayed response!
After a discussion with our developers, we have raised the development card to address this issue and make sure that split child order inherits the relevant tags from the parent order.
Unfortunately, due to the nature of this and splits working differently for 'auto' splits and 'manual' splits internally, this fix will be implemented for the 'manual' splits only for the time being.
If you would like to be updated when the fix is released, please raise a support ticket so it can be linked to the issue tracking system internally to receive an update.
In Error Prevention, we have Pick List selected.
When we split an order, we then have to 'pick' the item from the new order again, before we can process it.
Would be better if it marked the new order as 'picked' as well.