Thanks for the feedback!
Have you clicked on the footwear slot in the top-right corner of the screen? After picking up the leather boots, you'll need to select them from the dropdown that appears there to equip them properly.
Also, regarding durability, footwear durability only decreases when the additional stamina provided by the boots is being used. Once your stamina drops back to your base level (without the footwear bonus), durability won't decrease further.