The other way to think about it is that the price of many other things may have gotten cheaper (in terms of labor/capital) at the same time as fiat inflation.

But how can you untangle an objective production price from the fiat / economy it's produced out of?

If that were the case, you'd expect scarce but still produced assets (e.g. housing) to have both increased in price (due to fiat inflation) and decreased in price (due to production technology efficiencies).

Which one dominates to what degree likely depends on the asset.