The loot system in Sekiro: Shadows Die Twice can be confusing. Read this page to learn how to pick up gold and other items dropped by enemies.
Hold the interaction button (Square on PS4 / X on XONE) to collect loot dropped by fallen enemies. Your character will "suck" the loot. Amount of collected gold and items will be displayed on the right side of the screen.
You can't pick up items by just running over them. Remember about that when you are quickly moving through a location.
Loot from the chests is collected in the "traditional" way. Stand in front of a container and press the interaction button.