Confirmed and fixed. Your diagnosis was exactly right -- binding worked, pressing did not.

The cause: the touch gutter's 1/2/3/4 buttons exist so mobile and desktop resolve a number key the same way, but the mobile path was missing a step. Desktop goes skill -> BOUND ITEM -> quick slot -> action map; mobile went skill -> quick slot -> action map, with the item step absent. A quick slot is never keyed to a digit, so a potion on button 1 fell all the way through to the action map and did nothing at all.

Fixed on develop, not yet in the published build -- worth a re-test on mobile once it publishes.