dnd 5e – Is ammunition recoverable and reusable?

Ammunition is recoverable and usable.

At the end of the battle, you can recover half your expended ammunition by taking a minute to search the battlefield. PHB.146

A character who takes a minute to search the battlefield will recover half their expended ammunition.

To adjudicate what half of the ammunition is recovered, the PC who expended the ammunition will choose (since their character is the one searching, actively attempting to locate the ammunition).

A player should keep track of their ammunition unless it has been agreed upon before hand to use alternate rules for ammunition in a particular game.

Throughout this chapter, we use the term character sheet to mean
whatever you use to track your character, whether it’s a formal
character sheet (like the one at the end of this book), some form of
digital record, or a piece of notebook paper. PHB 11

The above passage denotes that a player is responsible for tracking and recording aspects of their character on a character sheet.

An easy way to keep track of ammunition is to enter it into the equipment section of your character sheet. For instance a quiver that has a capacity of 20 arrows, a player could write: Quiver; arrows 20/20

When they fire 6 arrows, it would be recorded as Quiver; arrows 14/20
If they take 1 minute to search the battlefield and recover 3 arrows, they would notate Quiver; arrows 17/20

Note there is no distinction between the original arrows and the recovered arrows, they are not damaged, they are functionally the same.