Why does brighter light release more electrons without increasing their maximum kinetic energy?

In the photoelectric effect, the reason brighter light releases more electrons without increasing their maximum kinetic energy is that light is absorbed in discrete packets of energy called photons.12

According to the quantum theory of light, the energy of an individual photon is determined solely by its frequency, expressed by the equation $E=hf$, where $h$ is Planck’s constant. Because each electron interacts with only one photon at a time, the maximum kinetic energy of an ejected electron depends only on the frequency of the incident light and the work function of the material, as shown in Einstein’s equation: $E_k=hf-\varphi$.123

Increasing the intensity (brightness) of the light does not change the energy of individual photons; instead, it increases the total number of photons striking the surface per unit of time. Consequently, more electrons are liberated, which increases the photoelectric current, but the energy of each individual electron remains unchanged.123