I'm not an astronomer or a physicist or anything of the sort, just a frequent reader of science fiction, but I believe the radiation you speak of comes from around the periphery of the black hole, outside of the event horizon.

-- Ron

Once anything is beyond the event horizon, even electromagnetic radiation ( light) can’t escape.

A lot. That's where most of the emitted radiation originates, just outside the event horizon. The force of gravity inside the EH exceeds that of normal stars, i.e. the force that ignites their fusion reactions. At the EH mass is stretched by gravity and accelerated to near light speed as it falls toward the point of no return. There's a lot of energy in play. There are also light years long plasma streams ejected from the EH at the poles of at least some black holes, at right angles to the accretion disk. Black holes are notoriously difficult to study. There should be brazilians of them but we have only actually found a couple dozen. The undetected ones are presumably not shining brightly.

I heard one report where somebody thought they did, didn't hear the follow up or confirmation. It's going to be weak and the radiation beams that are noted due to black holes are anything but weak.

No, matter falling towards the black hole winds up in an accretion disk around the black hole; it's moving fast (and it continues to have its momentum--unless it's aiming directly at the BH it's going to go into orbit). Moving fast it runs into other matter and heats up. If it's moving fast enough, it'll emit radiation to slow down.

However, the real emitters are jets and the BH's poles (since most rotate). Matter winds up crunched together (one way or another) and shot outwards at truly astonishing speeds, producing jets of matter and radiation.

Radio and other active galaxies very often have bubbles north and south of their central bulges thanks to the supermassive blackholes at their hearts, but even the Milky Way has Fermi bubbles because our central black hole Sgr A* used to be active.

Neutron stars and protostars also have binary jets. Apparently a white dwarf in the right configuration can, too.

However, the OP's confusion was around the fact that light cannot escape a black hole. This is only true past the event horizon, and for radiation to cross back over the event horizon it would have to be Hawking radiation (or some other phenomenon not known to science).

because one of the science sites I routinely visit had a decent article on just that: https://www.sciencealert.com/physicists-simulated-a-black-hole-in-the-lab-and-then-it-started-to-glow While they didn't create an actual black hole, they managed to create something with a lot of the properties of a black hole and in the process, confirmed Hawking radiation.

It seems to be what the philosopher Alan Watts called the tension between prickles and goo and would seem to confirm that while prickles arise out of goo, they also return to it, although for Hawking radiation to deplete an average galactic black hole would take more time than any of us has.

Matter getting close to a black hole can get heated up a lot and emit a ton of energy that we can see. It's only after it's fallen inside the "event horizon" does the radiation not have enough energy to escape the gravity well of the black hole. The neighborhood near a black hole can be quite lively and not at all dark.

Also please beware of the oft repeated descriptions of the "infinitely dense singularity" at the center of a black hole. All that means is that our current theories have no clue what's happening. Most reputable scientists (i.e. the ones I agree with) assume that our theories are just incomplete and that something exists at the center of a black hole to prevent an infinitely dense point ... we just don't know what it is yet.

This is my from my favorite (short & readable) essay on black-holes:

Black holes are fascinating.

From the little I remember of HS chemistry, atoms actually have a lot of "empty" space between the core and the electrons. So it might follow that if gravity is so intense in a hole, even the atoms would be compressed, but only to a point. IOW, going by the comment that there's no such thing as infinitely dense, we could end up with a plethora of protons, neutrons, and electrons all mashed together: atomic particles that don't make up atoms any more.

Ah, guesswork...