> ‘personal data’ means any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, an online identifier or to one or more factors specific to the physical, physiological, genetic, mental, economic, cultural or social identity of that natural person;

As I (entirely non-lawyerly) interpret it, you could not do a GDPR request to delete the counterparty emails, because those are things written by you, not information about you. However, an email in which you state "I broke my leg today." would be personal data, because it can be connected to your identity and is information relating to you.