When people talk about magic, they are referring to the strangeness of subjectivity, and what it is at a very fundamental level. I think a better analogy is being a Greek philosopher and trying to understand what matter is. No tool at the time can measure things in a way that would meaningfully lead them to an answer, nor did they have any theories where matter could be related to something they could study. So when we are confronted with the same situation, I think it's perfectly reasonable to assume that we, like them, are missing a massive piece of the puzzle. Calling it magic feels kind of right when it's something so large and consequential.
One of my favorite books is "The Man Who Mistook His Wife For A Hat" by Oliver Sacks [1]. It contains a number of amazing cases of neurology where someone has suffered a brain injury and the facade of our apparently sophisticated consciousness is exposed a bit. For example, a guy who suffered a stroke and became blind, but was unable to accept it, so he lied to himself and rationalized all the resulting outcomes. The rest of his brain was 100% normal, was an articulate, intelligent person in all other regards. But he would confabulate extraordinary excuses to maintain his belief system. That story just drives home how much we as humans are capable of rationalizing.
I don't recall if it was that book or another that describes Capgras delusion [2] where a person sincerely believes that someone they know intimately, say a parent or spouse, has been replaced by a doppleganger, but are otherwise fully rational. They can even state that it sounds crazy, but nevertheless it is true. Or a form of it where they feel this way about themselves, leading them to believe they are dead yet still animate, is the Cotard Delusion [3]. What causes it? When one looks at their mother, an array of neurological connections to associated feelings and memories are activated; apparently in these cases, that doesn't happen in the normal way, and rather than concluding that something went wrong in their heads, they experience as this person in front of my looks identically to my mother but must be someone else and that is why those feelings are not arising.
The point of these two small examples is that our experience of consciousness and "me-ness" is a self-consistent facade, not nearly as deep as we feel it is, as site-specific injuries can result in profound flaws in that system.
[1] https://www.amazon.com/Man-Who-Mistook-His-Wife/dp/149151407...
Starting with the laws of physics, no, we cannot in practice calculate a consciousness. But we also can't inspect a lottery machine and predict the balls which come out either. Nobody thinks the latter is is because lottery machines also contain magic, yet so many people think that of consciousness.
Could consciousness involve extra-physical explanation? Sure. But there there is an equal amount of evidence that lottery machines do too (i.e., none).