(The Burning Maze Spoilers) All I know is that the Sword of Juno(alongside Riptide) happens to be a (CANONICALLY-)Indestructible weapon, it's forged by and for the Gods themselves after all, so that rules out it being destroyed outright. So since it's not with the current owner up until TBM's events, either it's with Tempest to send to the New Romans themselves, or, and this is one of the worse possibilities NEXT to its destruction, 'Puny Boots' has it now(though at least his steed's dead too!)
Yes, I’m thinking that Caligula does have the sword and in my opinion if Reyna or any of the demigods that knew Jason see him with the sword they will absolutely have the will to murder that man and make sure he never sees the light of day again.
Because in my opinion there’s probably no way Tempest got the sword. Since, after all, he is a horse.