No, fiat is not commodity money as the value it represents for exchange is not the same as the actual value put into it during production.
Fiat is not a commodity, it is a license to a fraction of the total circulation social product.
>Just as money was backed by gold in the past, it is backed by oil now.
The petrodollar does NOT make burger fiat commodity money, it just forces other countries to hold USD in order to buy oil. There is not a fractional reserve system for oil vs dollars. And USD is obviously NOT the only fiat in the world, so you would have to explain how the Euro, Ruble, Yen, RMB, etc are all commodity money.
So let me repeat myself. READ MARX, READ CAPITAL. There is no way you would be conflating fiat and commodity money if you understood the literal CHAPTERS Marx writes about gold, metal, and commodity money.