The closest you could probably get to what you're looking for would be ta hiera (τα ἱερᾰ́), which referred to sacred objects, cults of the gods, and sacrificial victims. It is true that Greek religion was incredibly widespread, but what is likely more responsible is that religious practices were incorporated to an incredible degree into every aspect of civic life, far moreso than Christianity or Judaism today. There were no discrete lines between religion, science, medicine, and government, and thus no need for a separate term.

Additionally, compared to modern religions, the Ancient Greek religion was far more variable in terms of practice. There was no fundamental scripture along the lines of the Bible and there were very few universal rituals. Every area would generally practice sacrifices, pray pour libations, and hold festivals, but the festival dates and honorees, deities honored with sacrifices, sacrificial animals for said deities, etcetera varied wildly across locale. Zaidman and Pantel summarize these ideas well:

Greek religion may then fairly be said to be ritualistic in the sense that it was the opposite of dogmatic: it was not constructed around a unified corpus of doctrines, and it was above all the observance of rituals rather than fidelity to a dogma or belief that ensured the permanence of tradition and communal cohesiveness (Religion in the Ancient Greek City, 27).