I'm gonna preface this: IANAL either.

There are also different legal bases for different kinds of data processing. For example, I'm pretty sure ensuring your site's security counts as legitimate interest, and it's pretty common that IP addresses are stored and processed as such. You don't need to remove someone's IP from your access logs just because they asked for it, because your interest in keeping your site secure for both yourself and everyone else outweighs their interest in the privacy of their data. Legitimate interest is the fuzziest of the six legal bases and it doesn't help that advertisers have started attempting to qualify their BS as "legitimate interest" especially in consent forms (if they need your consent it's not legitimate interest, it's user consent, and they really should stop lying) but it still exists to keep things viable.

As a rule of thumb, if you're storing data to provide a service you need to export or delete that data upon request, and if you're doing anything over what's strictly necessary for providing your service you need to ask the user about it. And you're right, this applies to anyone whose instance is used by EU citizens.

Also, pseudonymous data still counts as personal data as long as the pseudonym can be linked back to personally identifiable information. You need to sever this link to comply with a deletion request.