It’s not surprising that ChatGPT has been accused of breaching the EU’s main privacy law – PIA blog noted that ChatGPT was a privacy disaster waiting to happen back in February. As the first complaint to be taken up by an EU data protection agency, this case will be watched closely by other EU Member States, and around the world. The Polish inquiry is likely to investigate many of the key GDPR issues that arise for AI programs and be used as a benchmark in future legal cases.
Email works the same way. Once your data is received by the other party, you cannot delete it.
Public mailing lists have a very similar behaviour to the fediverse’s. I am not aware of any credible GDPR cases against those, although it may happen down the line, we’ll see.