Reload 0 means drawing and firing/throwing can be done in the same action. What happens if you have a piece of ammunition in your hand and you don't want to attack with it or drop it? Example of how this could happen are Shuriken with the Returning rune, or Arrow Snatching, if the DM allowed you to keep the arrow instead of throwing it back. Would storing the ammunition require a normal interact action, or does its zero reload reduce that to a free action?
There is no specific "sheathe" or "stow" action, so they fall under Interact. While it's true Reload 0 reduces the actions needed to draw your ammunition, you are not using the Reload property when you are attempting to put something away. It makes no mention of benefiting you any time that you are not attempting to draw and fire/throw the weapon.
Stowing Reload 0 ammunition costs the exact same as if you were putting any weapon away. I'd even say this makes sense; you have your ammunition in a location that is easy to draw and fire, and you want to keep it that way. Being able to draw easily does not necessarily mean being able to stow easily, so you must be (somewhat) careful in how you place the object back within easy reach.
There is nothing in the reload rules that specifies that it takes less actions to sheathe an arrow or any other component used in a reload 0 weapon (such as a shuriken). So, by the rules as written, they'd have to stowed just like any other held item (what action that requires is a bit unclear, as Ifusaso points out in the comments, but an Interact action is the accepted standard and what your table seems to be using, so an Interact action would be required in this case).