It appears that if an NPC has a Trident enchant (such as Channeling), and they throw the Trident (successfully hitting the target), the enchant doesn't trigger.
I've tested it with enchants only a Trident can get, as well as putting enchants a Trident shouldn't get (like fire aspect), but the enchants don't work. Even though a thrown Trident with fire aspect, for example, doesn't set the target on fire normally, I think for the case of Sentinel, it should do that.
However, Drowned mobs are able to throw the trident and have the enchant still activate. Yet for NPCs, it doesn't seem to be the case.