A zygote is most certainly independent of the mother in the sense that the child and the mother are distinct members of the species. The child is not a part of the mother, but an independent (distinct) entity. The mother and child are distinguishable by biologists, by information theorists, by Thomistic philosophers, and by nutritionists in the south of France.
The child is most certainly dependent on the mother in the sense that this distinct, independent member of the species Homo sapiens cannot survive without constant support from the environment (another living person) that the child finds themselves dependent on. They are, as you point out, inseparable. But even birth won't solve this problem. From a societal perspective, even adulthood won't solve this problem for 99.999% of the human race.
neither our subjective nor objective experience of those cells today is equivalent to that of any human being around us. you just can't get to the conclusion you want with only biology and objectivity, because your key premise is neither an objective nor a biological axiom.