Pre-salvation confession MUST happen before salvation happens within time. Post-salvation confession is part of the life long sanctification process. In confession, we agree with God that what we did WAS a sin concerning a certain matter, and we agree with God that we shouldn't do it again. We ask for forgiveness and receive it. Presumably, we have learned something and will be a better Christian in the future. Before such a confession, there is sometimes/often an internal struggle about whether to agree with God or not. This is where we learn and are sanctified. If the confession is true, then we are forced to first admit it to ourselves. IMO, in this is great value.
Is is yet another mechanical exercise, entirely without meaning, like prayer?
I'm surprised that an Apostolic would accuse us of mechanical prayer. I think you guys have pretty much cornered the market in Christianity there. :) In fact, in my church, there is exactly ONE "mechanical" prayer that we say. I don't think you could say that.
It’s just that as the explanations about Calvinism mount, it seems that more and more of them lead down the road of mechanical performance.
Our prayers mean something to us because we believe that they actively work to help us towards our road to God and therefore our salvation. They do something and mean something to a believe trying to communicate with God, or else if they are truly mechanical, then they mean nothing since the intent of the individual is what matters.