Economically, mining is exploitation of any resource on a basis which fails to account for the full ecological formation costs of that resource.
In the case of petroleum, we can look at one ecological cost: time.
Petroleum formed over a period of hundreds of millions of years. It's been extracted by humans for a couple of hundred years. Even on napkin math, the time cost is being discounted by on the order of one million fold.
If the resource were so vast that it could not be meaningfully exhausted, this wouldn't be an issue. But we've hit peak conventional oil within numerous major producer countries, and quite probably the world, which corresponds to roughly half the total exploitable resource having been exhausted.
The economic theory most often mentioned for pricing of nonrenewable resources is Hotelling's Rule, formulated in 1932. I've read that paper numerous times, and the fact that strikes me most about it is that although it cites earlier economic works and numerous references of the author himself, it cites absolutely no scientific, geological, or petrochemical references. It's utterly devoid of any real-world grounding.
And we have pricing data to invalidate it, one of the most comprehensive being crude oil prices dating to 1870 or so. That's published as part of BP's Annual Statistical Review of Energy, showing both nominal and inflation-adjusted prices.
What's clear is that price does not follow the trend predicted by Hotelling, but rather reflects, at various times, unrestrained extraction (when the price collapses), various catellisations and embargos (when it peaks), and several periods of long-term managed output, during which it remains quite nearly constant. The longest and most stable such period was from the early 1930s to the early 1970s, following the establishment of regulated extraction in the United States (at the time the world's peak, and surplus-capacity, provider of oil).
Immediately prior to this period, following major discoveries and unregulated extraction in East Texas, the price fell from a target $1/bbl to $0.13/bbl, and finally as low as $0.02/bbl. The rational for pricing wasn't Hotelling's model, but the bare minimum price required to meet marginal costs of extraction.
More recently, in the 2000s and 2010s, what's emerged has been the flip side of demand destruction, where prices of oil can rise to the point that economic activity can't support them, and demand collapses, with it ultimately price (as more expensive marginal wells are withdrawn from production). Price has see-sawed between highs as the global economy surged, and lows, as it collapsed. Sometimes exogenously as with the 2020 global COVID pandemic, which saw US spot futures prices fall negative briefly at contracts expired and delivery had to be made --- there was no available storage and traders paid to have their oil offloaded.
The upshot is that extractive commodity prices don't behave as one might expect during periods of exhaustion. Rather than rising monotonically, they'll jump around on thin trading, surges in supply and demand, and external influences.
