Yes, that's correct. It doesn't "disappear".

I meant "gone for good" in pragmatic terms. The black hole's mass/energy definitely increases and its gravitational pull increases with everything that goes in.

I just meant that nothing will be escaping the Event Horizon. Matter can't because the escape velocity is greater than that of light, and nothing with actual mass can go 100% the speed of light no matter how hard it's pushed. Much less even faster. You could take a single electron or neutrino, use every last bit of mass/energy in the Universe as "fuel" to accelerate it, and it can never get to 100% of light speed. Just 99.9999(and a lot of 9's)% of the speed of light.

Massless energy/particles like photons can go no faster or slower than light speed. Since the Event Horizon is where escape velocity exceeds light speed they don't escape either.

One exception or caveat though.

There is Hawking Radiation. It's incorrectly described as the "quantum foam" that's everywhere at very tiny subatomic scales. Where virtual particle/anti-particle pairs pop up and cancel each other out. And some pairs at just the right spot along the Event Horizon are "split" allowing the the one just above the Event Horizon to become "real" and escape, while the other half goes down. And since even a black hole can't violate conservation of mass/energy the "real" particles that escape carries away a tiny bit of mass/energy from the black hole.

And the "quantum foam" is real enough. Very sensitive lab experiments, things with lasers, or devices cooled as low as possible with liquid helium etc. pick up it's faint "static hiss", which can never be eliminated.

But that description is an extreme oversimplification to the point of just being wrong. The "carries away a very tiny bit of mass-energy" part is correct though. Hawking himself owns much of the blame honestly. He was trying to come up with a simplistic explanation that a layperson and the press could understand.

The real mechanism for Hawking Radiation is insanely complicated mind bending math, and a combination of several physical laws, and how they interact under the extreme conditions near a black hole. The Heisenberg Uncertainty Principle, Maxwell's Laws of Black-Body Radiation, the Unruh Effect, and Einsteinian Relativity and what happens from various different reference frames in extremely curved space-time, and more, are all in the mix.

The net result though, is that black holes radiate away a little mass-energy as Hawking Radiation. It's a pittance compared to what they eat currently. And the Hawking Radiation is extremely weak long-wave radio photons from the viewpoint of an external observers reference frame for any stellar mass black hole or larger.

Over a very very long time though, a trillion-quadrillion years (whatever... just a very large exponential number in scientific notation) after the last stars in the Universe have long ago burned out, and there's nothing for the black hole to "eat" it will shrink and evaporate through Hawking Radiation.

The smaller the black hole gets, the "hotter" and shorter the energy, wavelength, or frequency of the Hawking Radiation photons gets, and the more it produces. And it grows at a gradual but exponentially increasing rate. Until it goes up in an enormous flash of gamma rays at the end.

Although, other theories of how the Universe "dies" and "deep time", might make slowly shrinking black holes that eventually go up in a huge gamma ray burst (sometimes called a Hawking Bomb) a moot point, if the expansion of space-time through "Dark Energy" creates the "Big Rip" where even individual subatomic particles cannot stay intact.

But that's all way way way beyond my understanding.