If the Sun were to suddenly stop nuclear fusion in its core, its luminosity would not change significantly immediately. The Sun's luminosity is a result of the energy released through the fusion of hydrogen into helium in its core. This fusion process is responsible for the Sun's steady output of energy.
If nuclear fusion were to cease, it would take a considerable amount of time for the effects to be observed. The energy produced by the fusion reactions in the core takes a long time to travel through the Sun's dense interior layers to reach the surface, where it is emitted as light and heat. This energy transport process is known as radiative diffusion and can take thousands to tens of thousands of years.
Therefore, even if fusion were to stop abruptly, the Sun would continue to radiate its stored energy for a significant period before its luminosity begins to decrease noticeably. The exact timescale for the luminosity to change significantly would depend on the specifics of the Sun's internal structure and the rate at which it is depleted of its stored energy.