If I use Greninja GX's "Haze Slash" attack to shuffle it back into my deck and also Knock Out the Defending Pokemon, who promotes a new Active Pokemon first?
In this case you promote first. Greninja GX is shuffled back in as an effect of the attack before KO's are checked, so it must be replaced before either player checks for KO's.
Source: Forbidden Light FAQ (2018-04-20), TPCi Rules Team (2018-05-03)