I wrote an essay about Black Holes back in the 70’s. I've no doubt they exist due to both observation and mathematics.
Observing stars orbiting Black Holes. Observing dust clouds being consumed by a Black Hole. Observing Tidal Disruption Events. Observing near light speed ejecta from the “poles” of Black Holes.
There are many things you can't “see” that have been proven to be real and actually effect the world/universe around you. Still, you can't actually “see” it, nor can you take a photograph of it.
What “proof” would suffice?
We can't see atoms either, however, with tools we can see them. One way is using radiation using atomic resolution microscope. It is also with radiation that we are able to say that we see certain things that generates the theory that Black Holes exist. But at this point it is still a working theory. That too is an honest statement.
If you are convinced, that is your right.
However, that was still an illustration, not a picture as it was presented to be. Which is what has sparked this whole useless discussion. The picture you presented is compelling but it still falls short of being proof.
I understand, once a person is convinced of the existence of something, they view compelling information as being that definitive proof. But the truth is that the proof remains just beyond grasp, and will continue to, until it can be proven, or perhaps a new theory is formed & presented that is even more compelling.
Einstein’s theory of relativity, both special relativity and general relativity, has been extensively tested and confirmed by numerous scientific experiments and observations. While no scientific theory can be proven with absolute certainty, the overwhelming evidence and consistency of the results have led the scientific community to accept relativity as a fundamental aspect of our understanding of the universe.
The same holds true will Black Holes. If you are incapable of accepting that as the truth, then that is on you, and nothing I can say can get you to admit the truth because you are a true believer. I certainly can't fault you, and I certainly am incapable of disproving the theory. But it still remains to be a theory. Even if there is compelling evidence, because the evidence is only compelling.
What “proof” would suffice?
Perhaps the deployment of a Hubble like telescope aimed at getting a much closer look at one, or both, of the two promising examples of what are believed to be Black Holes. We would hopefully collect much more evidence to see if the theory holds up, or not.
I might be a contrarian, but that is what science is all about. It's fine to accept a theory, even though it made be widely accepted, to keep pursuing to get to the truth, if possible.
This is even more important, because we have been told to accept the experts, or as they like to say, science, on such things as Covid & Covid "vaccines". I didn't just accept their science on that, and I refuse to accept, as fact, the science of Black Holes. I applaud the advances that have allowed to get to this theory. Very compelling, but still not proof.