For depression specifically, I could see placebo having another important effect. Agency. Taking action to resolve your problems feels good. Compare to rain dances, which while ineffective in bring about rain, surely helps reduce anxiety of the performer.
It might not even have anything to do with the drug itself: mental health issues tend to wax and wane on their own over time, so if someone happens to feel better right after starting a new medication, it's easy to think "oh hey this one must be working" and then that can trigger the placebo effect and turn into a positive feedback cycle.