Nice pic, I like existential comics. Also, I agree that there's a certain point where reductionism isn't getting you anywhere, I'm just pointing out that it does lead you to a single objective fact, the presence of your own self-awareness. And you're exactly right, we can observe people acting like sentient beings, but that is not sufficient evidence to make an objective conclusion that they are sentient. While I agree that other people are sentient, it's still useful because thats the question Miriam asks.
While you might view it as a truth that you can observe and then conclude that other people are sentient, Miriam might fundamentally disagree that people who have gone through the bulk matter transmitter are still ensouled, and in her eyes that concept of a soul is analogous to the self-awareness that the philosophers are talking about. Something completely unmeasurable, unknowable, and unfathomable that makes a person who they are.
Also, you don't need to start with the idea that zombies exist to conclude they exist, but either way its just a thought experiment. You can make up the basic assumptions is all I'm saying. Did Descartes really believe in the demon? Idk, but thinking about it was helpful for framing the question.
And, again, I don't think we disagree on the last point. Math is an approximation. A very useful one, but it isn't representative of what's occurring 100%. In the same way, just because you can observe a zombie doing all the correct things doesn't mean you can ever or will ever have a way to measure the presence or absence of the soul or self-awareness.
To most people, you and me both, its a pointless question. But to Miriam its crucial, because she believes in souls. Even if you don't care, she does. This isn't something she can handwave with math or science or whatever. Miriam believes there are real, eternal, consequences to losing your soul and that the bulk matter transmitter might cause just that.