You are right, I should clarify this. For the authentication server the time required jumps from close to nothing to a few ms. For the attacker, the time jumps

You are right, I should clarify this. For the authentication server the time required jumps from close to nothing to a few ms. For the attacker, the time jumps from a few hours or days to a few years or decades. This asymmetry is what I meant when I said that it's a drastically different picture. Peppering is applicable to all hashing algorithms unlike the specific parameters you mentioned.