“Attorney-client privilege” only restricts the attorney or law firm from divulging the information. The client is free to speak as they desire.

The same applies to “doctor-patient confidentiality”. You are free to tell anyone you want to about your entire medical history, but your physician and their staff are prohibited from doing so.

Deliberately or carelessly, in either situation you retain the right to share the information, and the consequences of doing so are yours alone.