You shouldnt need to use any playerstate… use playerstate based ASC only if you need attributes and abilities to move with the player. Your abilities/attributes reside on your pawns.
if you just possess the NPC pawn with your player controller you should have access to it’s ASC and GEs/Abilities should network over at that point with Mixed mode because it will be relevant to the connected player controller at that point. You should still use AbilitySystemComponent->InitAbilityActorInfo(this, this);
You could try Full rather than Minimal replication mode for selected units and see what is available on the client. I think you should be able to access cooldown info as it should replicate to all clients under Full, not sure if GAs will replicate over without the client player controller though.