What physical driver causes increased mass to dramatically increase a star's luminosity?

Increased compression raising central temperature and density, accelerating fusion exponentially.

The fundamental reason for the dramatic increase in luminosity when a star gains mass lies deep within the stellar core, driven by gravity. Adding more mass increases the gravitational squeeze on the core, resulting in substantially higher central temperature and density compared to a less massive star. This extreme environment causes the rate of nuclear fusion reactions—the conversion of hydrogen into helium—to accelerate at an exponential rate relative to the mass increase. This highly sensitive relationship between core conditions and fusion rate is what translates mass directly into vastly higher energy output and luminosity.