Article 79, "Right to an effective judicial remedy against a controller or processor," seems to say that individuals can sue controllers or processors. This may be limited to cases where the regulatory agency does not find in the data subject's favor? https://gdpr-info.eu/art-79-gdpr/

Article 82, "Right to compensation and liability," begins with the text "Any person who has suffered material or non-material damage as a result of an infringement of this Regulation shall have the right to receive compensation from the controller or processor for the damage suffered." https://gdpr-info.eu/art-82-gdpr/