After my store closed I went to reclaim my items but the NPC said that I didn't have enough space to do so. Decided to open four free slots in the equip/use/etc tab, which was enough space and yet the NPC didn't allow me to reclaim my items. Do I have to open more spaces or is this bugged?
You probably had more items to be returned to you, so free up more space. It's not necessarily 4 slots for eqp/use/etc tab, that's only for quest rewards. You might have placed more than 4 item in a particular sub tab, hence freeing up just 4 slots might be insufficient.