You seem to think philosophy of science hasn’t advanced beyond Hume and Popper. That’s dubious, but there’s no need to get into that. You say, “Even if we did have some degree of confirmation though it still wouldn’t be much.” So what would you say is the degree of confirmation of the statement that species evolve in part by natural selection or that the universe is older than six thousands years? If you say, “not much,” I doubt more than one percent of scientists would agree with you. If theories of truth and probability can’t yet explain the difference in value between saying, “The universe is billions of years old” and “The universe is only several thousand years old,” so much the worse for those theories.
But I agree with the thrust of your criticism of science. If you check out my blog, you’ll see that I promote something like Lovecraft’s cosmicism and that I criticize naturalism, secular humanism, and the correspondence theory of truth as being overly optimistic and hubristic. So I agree we shouldn’t expect that human knowledge will completely mirror everything that exists. I actually take a pragmatic view towards science and truth.
When you say that “science doesn’t entail naturalism,” you leave out the “methodological” part from my statement. I agree that scientific methods don’t force scientists to be metaphysical materialists or to deny that people can walk on water or live after the body’s death. Practically speaking, though, scientists are committed to methodological (not metaphysical) naturalism. Scientists will tackle any miracle claim by trying to naturalize the phenomenon. Once you naturalize the phenomenon, the claim is no longer about a miracle in the theological sense, since the event no longer transcends nature.
You say, “Science is mute on topics which are not falsifiable and not empirical.” I agree that scientists tend not to talk about poetic or religious issues, since those issues tend not to be expressed in scientific language. Most scientists would take that to mean that those issues should be dismissed, that those phenomena are subjective rather than objective. Of course, there are exceptions such as Francis Collins, but most scientists are in fact atheists, especially at the elite level.
In any case, that’s a tempest in a teapot, because there’s philosophy in addition to science. Scientists may not speak on those issues, but philosophers are free to do so, and most living professional philosophers are themselves naturalists and atheists.