The PlayStation messenger system does not have a means to delete already sent messages. PlayStation support refused to delete my messages containing personal data during a chat request. Their EULA/privacy documentation seems vague and doesn't quite explain this as far as I could understand it, and regardless, are there not laws in California that overrule this corporate policy sidestep? What recourse do I have to ensure my messages are removed? Their support team indicated there is a way for engineering to do so, but refused to process my request and use that method.
Your personal data, in all likelihood, belongs to Sony. As a result, you are asking if there is a way to force Sony to delete its own property, which you consented to it giving to it. I doubt that is possible.