I humbly thank Amy Dakin for her A2A, but I am a dunce as to Ancient Greek religion. I’ll note one odd thing though.
I’m not sure of this one thing, and I’m happy to be shown to be wrong.
In a few questions, I tackled the question of “what’s with the meaning of agape”, by going to the Diccionario Griego–Español as Ground Zero for the latest definitions not overly coloured by Christian theology. See Nick Nicholas’ answer to In the New Testament, what different semantic shades can the verb agapao (“love”) take?
Now, I noticed an odd thing with agape. It could be directed to pagan deities or the Christian deity; but as a noun, it is not attested before the Koine; and in particular, it is addressed towards “Oriental” or Egyptian deities, rather than native Greek or Roman deities. The verb agapaō is also plentifully applied to God in the Septuagint.
And in fact, the nominalisation agape itself is no earlier than the Septuagint.
Now, this could be coincidence, and I’m happy to be corrected; but I don’t see clear evidence that the Ancients used either agapaō or phileō (or philia) to refer to their attitude toward the Gods. On the contrary, I see Aristotle, Topica 105a, pose the question “whether or not one should honour (τιμᾶν) the gods and love (ἀγαπᾶν) one’s parents”.
My suspicion, then, based on superficial knowledge, is that the Greek gods inspired awe or reverence, but not love; that feeling love towards a god was a Hellenistic, Jewish, and Christian thing.