Assuming the second from the bottom is a metal file based on the form; maybe a scraper of some sort. A metal file seems like a very rare commodity right? Scrapers and stone flats seem far more practical in most situations IMO.

Iron production in the Roman Empire was crazy high - wouldn’t be matched again in Europe until the 16th century AD. Rome’s iron output was around 10 times the amount produced by the comparably complex and large Han Empire of the (relatively) same period.

So it could very well be a metal file! Metal tools that didn’t need to be metal for basic functionality wouldn’t have been dirt cheap, but also wouldn’t have been prohibitively expensive.