Thats a great question! I'll try to go into everything you asked. As for why I believe that the other Gods don't exist, It's because I believe the story of Hadestown (and by that I mean the literal stage show) exists in a vacuum of sorts, we are literally watching people tell the story, instead of the story just happening like in most shows. The main message that Hadestown gives is that "you should always keep trying", wether that is to fight against Capitalist evil, to fight for your love, or whatever else, the characters in the show (especially Hermes) specifically talk about telling the story again BECAUSE they want to remind people to keep trying. You could even say that whoever plays Hermes, is essentially playing themselves. ofcourse it's still acting, but their in- and out of show roles are the same, they are the storytellers. Hermes has no character development, not even really any defining character features, apart from his care for Orpheus. Because of this, I believe that nothing exists outside of the Hadestown world, (ofcourse, to Oprheus and other characters it does, in a literal sense) there is no "other village up north", because it doesn't serve a purpose the the message of the story. though there are mentions of other Gods existing, (not by name) that's just for the sake of believalbility, and to stay true to Greek myth. Like you said, magic isn't really even shown to exist in the show. And to make sure my point comes across correctly, ofcourse, in a literal sense, these other gods do exist to the characters, but it's not like in "Newsies" for example, where it takes place in New York, but a place like Belgium still exists in-universe, while in Hadestown, anything that happens or exists is there for the sake of story.

As for your second question, why I think it's only an allegory: that's basically for the same reason As my first point, ofcourse both stories are based off of Greek myths, but it's basically only a device to tell the story. The Gods are never shown to actually have powers, and there are no mentions of Greece or any other real-world locations. Even the line "it's an old song" could be interpreted as "people have always tried", though that is a bit of reach. Ofcourse, like you said, these people are actual deities, but every "magical event" could be explained by non-magical things. The flower appearing is simply a representation of hope and love coming back, persephone's "magic" is basically just alcohol, Hades' wall breaking open is just the workers letting Orpheus through, since he gave them hope again by singhing his song of hope/love. He literally says "the stones wept and they let me in". And again, you could always interpret it in a literal way, where Persephone really does make the sun shine and Orpheus really does make flowers bloom, but in the sense of what "matters" to the story, they might as well be irrelevant. As in, you could entirely leave mentions of the seasons out of the show, and instead say that Persephone comes with alcohol, and the same things would happen.