Confession is the religious practice with the clearest secular successors, and the lineage is not merely a metaphor.
Psychoanalysis took the structure and changed the theory. A person speaks at length about themselves to a trained listener who does not judge, in a fixed setting, at regular intervals, under confidentiality, and the speaking is itself held to be curative. The debt to the confessional was noticed early and usually by critics, and the analytic tradition has been ambivalent about the comparison ever since. The differences are real: no absolution is offered, and the material sought is what the speaker does not know about themselves rather than what they are concealing. The form is nonetheless recognisable at a glance.
Twelve-step programmes are more explicit about it. The fourth and fifth steps require a searching moral inventory and then the admission of its exact nature to God, to oneself, and to another human being. The programme began in an evangelical Christian context and kept the shape while making the theology optional, which is why it transplants so readily.
Truth commissions apply the same logic to a whole society. South Africa's Truth and Reconciliation Commission granted amnesty in exchange for full disclosure of politically motivated crimes: confession with absolution attached, made public rather than private, and administered by a state. It was criticised on precisely the grounds religious confession has always been criticised, that it can substitute for restitution and let the guilty settle too cheaply.
The comparative point is that the underlying claim, that saying the thing out loud to another person changes something, has outlived the theology that once justified it, and has been rebuilt from scratch by people who would not describe themselves as religious at all.