The middle click menu would have another point: "Provider". Then this item would be refilled into the players hotbar when the items count in a stack in the hotbar was not stack-max-size.

That way a player could always have 64 steaks and 64 torches in the hotbar as long as the PlayerStorage holds such items.

Maybe it is already there and I jsut didn't find it?

1.3.3: Yes it is there and I didn't find it directly after the update. Thank you very much!