Each Bitcoin is basically a computer file which is stored in a 'digital wallet' app on a smartphone or computer.
IMO, "Each bitcoin" can not be classified as a unique computer file. The "amount of your bitcoin" is defined by the spendable UTXOs associated with your wallet, which in turn is derived from your private key.
This makes it possible to trace the history of Bitcoins to stop people from spending coins they do not own, making copies or undo-ing transactions.
People cannot spend the coins they do not "own", not because of the ability to trace transaction but because every bitcoin is locked by the owner's private key that only the owner is supposed to control.
"Making copies" or "Double spending" is not possible because confirmed transactions become part of the longest chain making it impossible to change the references to previous transactions.
"Undoing transactions" is again a result of impossibility of modifying the blockchain without owning a great amount of hashrate of the Bitcoin network.