I must have missed something, but when did Stormbreaker become Bifrost?

How does Gore know the Bifrost is the key, Stormbreaker is the Bifrost, and Thor has Stormbreaker? More generally, why is Gorr going after Thor in particular?

Does Zeus' lightning also allow you to cross the universe? How does Jane Foster manage to cross the universe from Earth to Eternity, on the back of Valkyrie's winged horse?