The gods are dead. Dead but not gone, their bodies remain in this world, the divine essence given physical form. Their believers are those who crave the glorious visions of heaven that consuming this essence grants, their churches the organisations who help to satiate these desires – and who profit off doing so. As for their clerics, they partake of the divine essence for other reasons, for it alone grants them their powers.
God drugs are a special form of holy symbol. Whenever a cleric of a dead god would need to use or present their holy symbol, they have to consume one dose of divine essence instead. You also need to consume one dose of divine essence whenever you wish to prepare any cleric spells.