A cr2032 has somewhere around 200mAh. The low-power ESP32-C3 uses somewhere around 20mA when its radios are off but the CPU is running and peripheral clocks are running, which gives a roughly 10 hour runtime. This calculation ignores the fact that the battery's voltage will drop below where the ESP browns out before it has delivered all its power (or assumes that it's regulated up at perfect efficiency), but most cr2032 batteries are a bit above 200mAh so it probably mostly evens out.

Though note that for most of its life, the cr2032 will deliver slightly below the ESP's minimum spec of 3V. From experience, that's not really an issue.

If you can get away with spending most of your time in the ESP's deep sleep state however, battery life is gonna be way better, and that's probably what you'd want to do if you're using a cr2032. In deep sleep, the ESP32-C3's data sheet says it consumes around 5µA (0.005mA). With 200mAh, this gives a battery life of 40 000 hours, or 4.5 years. At those time scales, battery self-discharge becomes relevant, so let's say a couple of years.

So a decent mental model is: you can do a few hours of cumulative compute over the course of a couple of years.

Unless you decide to boost the voltage of the cr2032 to be within the ESP's spec. In that case, the whole deep sleep discussion might be moot; I suspect the regulator's own power draw would absolutely dominate the 5µA of the ESP. But I'm not super familiar with the world of power regulators, maybe there are ultra low power regulators which can do the job with minimal losses even in the µA regime.