The authority is still probably the most nebulous part of this whole deal, since everybody only ever talks about them using their headcanon and passing it off as that is what is collectively established. Essentially you have a bit of a choose your character situation.
Titanium White- everybody actually seems to agree on him being here for once, what they don't agree on is if he is Bob Ross, Senator Armstrong, or any other character or mix of characters.
Red - Well whatta you know, this lads my own creation, shamelessly ripped off from Diavolo than expanded upon this metal is an eternal rival to Gold and vicisously protects the truth of his true nature and identity, since no one knows what metal he is they just call him Red.
Gold - The main antagonist, caused the events of the AU by proclaming that all other Golds be scrapped or discontinued and that he, in his, vanity, is THE Gold. Essentially DIO, Fulgrim, and all types of vain charismatic bastards, but unlike those assholes he does genuinely want the best for the metals.
Plutonium Green - his power is maximum, big ol radioactive angry boy who has a hate boner for gems. Depictions range from being a skeleton monk to a pretty boy strategist.
Cabon Black - probably the most controversial possibility for authority member due to carbon not really being considered a metal, is actually a fuck ton of steels fused together and loves fighting more than anyone else, sundowner type of guy.
Silver - probably the least known authority choice he is the most skilled swordsman in the setting due to his mysterious travels outside star maps but he is foremost a teacher, has had his memory wiped twice, once by TW and once by Red. Has a Jetstream Sam thing going on.