I'd expect to see items in my ship storage in the Coretechs listings.
I'll create a ticket in sec.
To see them or to transfer them like regular storage?
Seeing them I can understand, shipping them from ship to ship or to regular storage I don't see.
I assume that anyway, seeing them would be a first step.
IMO, this makes sense, in order to provide the total overview of what you got and where.
perhaps as a subsection of inventory management? much as how you can filter the view by type/tier/etc