Now when it comes to deconstructing things like how dogs were actually regarded in Greek (and perhaps Sumerian) religions, you’d be better off learning from surviving extant Japanese and Chinese data however involving foxes. There’s a healing goddess named Gula but her evil counterpart (of sorts) is Lamashtu. A similar pattern occurs for both Artemis and Hecate.
By analogy, in Japan though Inari’s associated with foxes yet foxes themselves are sometimes feared for witchcraft. (Hecate’s also associated with the same or similar things.) The problem’s that both Iraq (Sumeria) and Greece have converted to Islam and Christianity respectively with Turkey and Syria being the odd middle grounds when it comes to Crypto-Christian but technically Islamic communities.
So such paganism would’ve been marginalised and reduced to folk demonology, had it ever survived at all. But when it comes to demonising dogs (and cats to whatever extent) especially by Islam and Christianity, it becomes either a grey area or chicken or egg dilemma where it’s hard to tell whether if it’s officially endorsed or not.
There are attempts to get rid of the following for Saint Guinefort (a dog) just as there are attempts to stamp out fox worship in China. Whilst Japan’s a good example of a secularised heathen country (Turkey’s a secularised Muslim nation), China’s trickier to define due to Communist atheism in the past and is now rediscovering religion.
This makes Japan a better candidate to reconstructing Greek polytheism as animism and polytheism in Shintoism’s still a thing. The fact that anything ranging from wolves (Apollo) to celestial bodies are still worshipped and considered divine. Japanese and Chinese folk beliefs about foxes can be applied to how Ancient Greeks regarded dogs as.
That dog and fox witchcraft are equally found in some Japanese regions and that there’s a Greek breed called Alopekis’s not much a stretch to assume that a small dog would be mistaken for a fox.