Has there been a study of correlations? What I am aware of is that many studies report quite high failiure rates but I don't know of any study that tries to asses if success or failiure of treatment A predicts success with treatment B. This could give a hint to the nature of depression.

This is a very good question that I don't know the answer to. Anecdotally, it seems that people try X, find that it doesn't work, then try Y, and find that it does work.

The mere fact that there is no difference in effect of any one technique or the other is massive evidence that it is not the technique that is benefit but something else, like simply sharing feelings with a person.

One would have to look at the details regarding what's meant by "no difference in effect." It could be that the error bars around the effect size of each are really large and overlap to such an extent that there's a ~50% chance that intervention X is better and a ~50% chance that intervention Y is better, and that this gets labelled "no difference in effect" even though it could be that there's a big difference in actual effect size.