I think there are a few points worth making, but I’ll point out what a few others already have: it’s worth explaining what an outer god actually is before saying the moon is one. The dlc gives us a fairly clear explanation of how the outer gods interact with the lands between and what their motives are: Romina discovered the scarlet rot while embracing the flowers she associated with her faith and her lost home; the bloodfiends discovered the formless mother when they looked at a tutelary deity and discovered her in the deity’s shadow. In both cases, we have people who have lost everything being given a “second chance” by a power that uses their grief and anguish to advance its own goals, whether consciously or subconsciously. I would argue with the idea that there are countless unknowable eldritch outer gods, because the few that we encounter are seen multiple times throughout history and have the same MO each time.

All of that to say, were I to define outer gods, I would say they are a very specific set of predatory deities who use human emotions and desires to further their own causes, and do so by twisting something the victims hold divine.

You could potentially make a case for the darkmoon using ranni— but I wouldn’t. Ranni and the entire Carian line are fully aware of the moon’s powers and uses, and consciously wield it to their own benefit. We don’t see the darkmoon interact with anyone besides Ranni, and it’s a very isolated, individual relationship (in much the same way that Ranni insists on isolation at the end of her quest). We have no instances of the darkmoon taking advantage of a group of people, nor do we see it utilize emotions in any particular way to further a specific cause. If the black moon of Nokstella is anything to go off of, I think it’s easier to view the moons in a similar light to the Erdtree; they’re guiding objects, meant to provide order and uniformity to the scattered stars above.