My understanding is that this just changed and now psychotherapy is paid by basic insurance and got taken out of supplementary. One needs a prescription from a GP.

Terence here: https://www.bag.admin.ch/bag/fr/home...erbringer.html

At its meeting on 19 March 2021, the Federal Council decided that psychologists and psychotherapists will be able to bill their services to the compulsory health insurance scheme on an independent basis. A medical prescription will be required