What appears to be the central energy-generating system or engine that is producing prodigious amounts of energy in the centers of galaxies, active galaxies and quasars?

A massive black hole uses the energy from falling objects to cause particles to become so hot they emit X-rays (not just the visible light from meteors), and if they are not directly captured, they could be flung out with such speed and energy that they create powerful jets. In the case of Earth, the gravitational field is weak but still provides enough energy to break an egg that rolls off your counter or make meteors glow as they arrive from space.

Upon observing this activity and calculating the energy needed to propel it, astronomers find that they must summon a massive black hole because no other object appears to be able to generate enough energy through its gravitational field.

The Milky Way's central black hole isn't currently absorbing enough material to produce the amazing results described above, but we "see" it by observing the orbital motion of nearby stars and other matter, which is so fast a large, compact mass has to be holding things close. See https://tutor.hix.ai for evidence of such black holes from our own galaxy (as well as some others).

The central energy-generating system or engine that produces prodigious amounts of energy in the centers of galaxies, active galaxies, and quasars is believed to be supermassive black holes accreting matter.