oh that's an interesting one, as far as my testing went you couldn't pickup stuff when full. Press F to open your full inventory though if you think the taskbar is the only inventory.
Didn't know that was a button, everything makes sense now. I originally picked it up when my inventory bar was full so it went into the slot in the full inventory. Unsure if I just glossed over it but you might want to highlight how to get to the full inventory. The UI is made in such a way that I thought the item bar was an intentional limit.