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I dont think that stigma is going to get any better any time soon (at least in the US). The past year has given me significantly less trust that anything medical remains private; i have no trust that things said in confidence will not be weaponized against me by the current government. There have already been cases of states demanding medical records for pregnancy, abortion, and transgender records, and texas actually got their hands on some records IIRC.
My therapist says she takes a bare minimum of notes because she understands the fear people have of private info getting leaked. Maybe someone worried about that could ask about their notes process during the therapist-finding stage.