Answer

That is a good point. From the perspective of a moral atheist (a state of affairs that in my view is an oxymoron, but it exists), there is a moral prohibition against murder, but no moral prohibition against suicide. From his perspective, a person has absolute ownership over his own life, and no one else has the right to violate that. However, from a religious perspective there is room to see this as a moral prohibition as well. This really is a rare example of a moral principle that is not universal but rather Jewish (or religious). I had not thought of that. Still, one should remember that this arises only because there is an inconsistent element here (an atheist who is committed to morality). Were it not for that, there would be no disagreement here.
And perhaps one could say that the prohibition against murder itself is divided into a moral prohibition that exists only in relation to another person, and a religious prohibition that exists also in relation to oneself. Meaning, even if the whole world were consistent and understood that there is no morality without God, the prohibition against suicide still would not exist on the moral plane. Rather, according to this, there is here a religious prohibition that is not halakhic / of Jewish law (that is, one that exists even without the halakhic aspect). A kind of going beyond the letter of the law or pious conduct. In that case, the prohibition against suicide turns out to be a measure of piety built on top of the halakhic prohibition against murder, but it belongs to the religious plane and not the moral one.
And indeed, it seems that this is the difference between “You shall be holy” (according to Nachmanides there) and “You shall do what is right and good.” The first is a religious measure of piety, that is, extensions of moral commands, whereas the second is a moral command detached from Jewish law.
An excellent comment, and it is definitely worth further thought.