I bought it from a trader at the Concord, and while the cash got deducted from my account (go figure), the item disappeared the moment I switched to my equipment tab. Is it a bug? Am I doing something wrong? Is there a way around the issue?

Look if it moved to the equiped items.

Items equipped in the quick slots disappear from the inventory and are added to the total amount of the corresponding quick slot as soon as you quit the trader menu.
Completely confusing, isn't it?
They should show you the equipped items during trade, but you must have noticed equipped items are not even mentioned, you don't know wether you own one or a hundred of them.