I'm pretty sure that's not Stormbreaker in the picture, besides Stormbreaker is destroyed and I doubt even Phastos could repair it.
I think the God of Hammers will be someone we already know or a brand new being but either way they will be a God of some sort. Phastos like all Eternals are not gods but long lived superpowered humans due to alien interference.
I'm willing to bet that Mjolnir is the God of Hammers! Mjolnir is it's own entity! I mean how can that not be an obvious theory is beyond me....