It's hard to say whether there's metaphorical, allegorical or even literal meaning to the vultures from what we know so far, Nikos obviously held some familiarity with the sighting, but overall vultures aren't particularly common in Greek myth, save for two particular figures: Ares and Tityos.
The vulture is Ares' patron animal, as they would always be found feasting on the corpses of fallen soldiers after a war. Given what Ares is about and the kind of bloodthirsty psychopath he is in literally every interpretation, I'd say it's probably unlikely the vultures are to do with him? Plus he was unsympathetic to Asterion's plight, so... yeah.
Tityos was a giant who faced the wrath of the Olympians in pretty much exactly the same way as Prometheus did, except in Tityos' case his organs were to be feasted on for eternity by--explicitly--vultures. At face value, the story doesn't seem to bear much connection to MH. BUT...
Tityos was the father of Europa... And therefore King Minos' grandfather... And therefore... Asterion's great foster grandfather AND Nikos' distant great uncle.
So there's that connection, but it's still I think a somewhat distant one. It's kind of a funny coincidence, though!
Edit: There are actually multiple Europas in Greek myth, only one of whom was sired by Tityos. Whether or not they are unique individuals or varieties of one amalgamated figure is really anyone's guess. Greek myth be weird like that.
I'm thinking their presence was more about the appearance of real, untainted life above the corrupted desolation of the valley. Nikos' moment of familiarity felt more like a reminder of life outside the valley, since he's had to live in it alone for the whole length of the story.
That's just how I interpreted it, anyway :)