In order to make gamepad controls work well, there has to be a way to have a current button highlighted. Moving up/down/left/right would move to a different button in that direction, and pushing a chosen gamepad button should click the button. Not every button should follow this scheme: some buttons should not be part of the button group that can be selected. Others should be part of a different button group. For example, interacting with a shop should let you switch between button groups: one is the shopkeeper, and one is your inventory.
Inventory items should also be selectable like buttons. Having a UI button or inventory selected should show the tooltip for it.