It is true that black bodies absorb all incident radiation and emit radiation themselves. However, it's important to understand that black bodies do absorb and re-emit their own radiation, including the Sun. The reason we can see the Sun is because it emits a tremendous amount of radiation across a broad spectrum, including visible light. The Sun's emitted radiation is not immediately reabsorbed by itself, but rather travels through space and reaches our eyes or other detectors, allowing us to observe it.
The reason we perceive the Sun as a source of light is because it emits a continuous spectrum of radiation, including visible light, due to its extremely high temperature. This emitted light is the result of the Sun's internal processes, such as nuclear fusion in its core. The light emitted by the Sun travels through space and eventually reaches the Earth, where it can be detected and observed.
The concept of black bodies absorbing all incident radiation applies to the equilibrium state, where the absorbed radiation is in thermal equilibrium with the emitted radiation. In this state, the absorbed radiation and the emitted radiation balance each other, resulting in a steady-state temperature. However, this doesn't mean that the black body absorbs and reabsorbs its own radiation in a self-contained loop that prevents any external observation.
So, while the Sun can be considered a black body that absorbs and emits radiation, we can see it because it emits a significant amount of radiation, including visible light, which reaches our eyes and allows us to perceive it as a luminous object in the sky.