The GDPR extends far beyond the US notion of PII. As I understand it, it covers basically all user-submitted or user-related data if it's possible for that data to be hypothetically tied to an individual in the EU (even if that can be done without your service holding traditional PII).
> As a private individual I suspect you would not have much to stand on if the NSA knocked on your door.
Yeah, a federal agent with a wrench can do anything they want to me (https://xkcd.com/538/), but I'm trying to figure out my options.