Nangnang is a former grung who is now one of the “Nine Trickster Gods of Omu,” which would imply that Nangnang is a god rather than an archfey. However, implication is all we have—the label of “god” was simply what the Omu called the beings they worshiped, after their original patron deity, Ubtao, left. We do know that the trickster gods were relatively poor at the whole “god-hood” thing, and were only able to supply spells to a limited number of clerics. That could just mean they were weak gods, or it could mean they were some other form of power, not properly gods, and that was the source of the difficulties.
Note that the Forgotten Realms is a mythopoetic setting—believing something can make it true. If they Omu believed the trickster gods to be gods, they could have become gods even if they were not originally. So a cleric of Nangnang would have been more likely than a warlock, but a warlock is not implausible; that would be up to the DM. So would what sort of patron each would be—archfey makes a certain amount of sense for “primal spirits,” but it’s not defined anywhere.
Tomb of Annihilation spoilers to follow
Of course, all of that is at least somewhat moot, since they’ve all been killed by Acererak of Tomb of Horrors fame and dead gods don’t really work the same way as living ones. Dead gods don’t grant spells, which makes it very difficult to be a cleric of one. In fact, in previous editions, there was a specific class known as the “ur-priest” that steals divine magic from others’ prayers—usually due to evil ambition or hatred of the gods, but sometimes because the god the ur-priest is actually faithful to is dead. If I were the DM, I would have a cleric of Nangnang to be an “ur-priest,” using the cleric stats but in-character being slightly different—and something other clerics are going to very much dislike.
That still doesn’t help you with your warlock. Sorry, I am getting there.
The thing is, even though Nangnang is dead, her spirit has been bound to the Tomb of Annihilation, and can still influence matters. She cannot grant spells, which means she cannot manage a flock of the faithful. But maybe she can bind her little (relative to a god’s) power to one specially-chosen mortal, in a fashion far more intimate than a typical god–cleric relationship: by becoming that mortal’s warlock patron.
The warlock could be familiar with the situation, and know that Nangnang is weakened and cannot properly be considered a “god” at all, and that they are not a “cleric” but instead a warlock. On the other hand, this warlock may well think they are, in fact, a cleric, that Nangnang is a goddess who is granting them spells and other divine boons as normal for a cleric—because they don’t know what “normal” is for a cleric. Any discrepancies between this “cleric” and an actual one would just be chalked up to being different faiths. Any scholar who tries to explain how divine magic works and how what the “cleric” receives cannot be that may be ignored as simply being some foreign snob who doesn’t get how we do things here in Omu. And so on.
Either way, one of Nangnang’s likely goals for their “cleric” is to have them restore her to her life and divinity. That can be done: Bane was killed during the Time of Troubles, and then resurrected himself through his son, the lesser deity Iyachtu Xvim (killing his son in the process; Bane is not a nice god). It helped that Iyachtu Xvim had inherited his father’s divine portfolios and worshipers, and that worshipers of Iyachtu Xvim basically all wished they still had Bane—making it relatively easy for Bane to replace his son. That said, the incident gives some hints here: the two aspects of D&D divinity are portfolios and worship. Nangnang’s spirit may well have retained her portfolios; it does not appear that any gods have stepped in for the Nine Trickster Gods in their absence, as the Nine did themselves when Ubtao left. So the main trick here is getting her former faithful to once again worship her. With enough faithful—and, most likely, the right ritual, involving powerful artifacts likely related to Nangnang—she could be resurrected as a goddess. How, exactly, that would happen is very much up to the DM.
Important note, perhaps, though: Forgotten Realms is really serious about every mortal worshiping a god. It’s super important, and the punishments for being without a god—a living god—upon death are really unpleasant (I am still trying to look up whether the character would be considered False or Faithless in this situation—but neither’s good). Someone worshiping Nangnang while she is dead is potentially in for a really unpleasant surprise when they die. On the other hand, it is not-at-all uncommon for other gods to swoop in and scoop up misguided mortals’ belief, so someone who thinks they worship Nangnang may find, upon death, that their worship has actually been going to some other, similar-ish, deity. That saves them from being False or Faithless, but it might mean an afterlife quite different from the one they imagined. So not only does this warlock want to resurrect their goddess out of love for her, belief in her, and/or desire for the rewards she would bestow upon them, they also have some serious dangers to avoid by making her a true goddess once more. Death on this particular quest could have consequences even more dire than it typically would.