True, though the "owners" (what's the term I'm looking for here?) of some channels do public logging

e.g. https://irclogs.ubuntu.com/

You’d have the right to request removal of your messages from those logs.

I'm sure most sizable IRC networks have some level of logging if only to validate claims of spam or rule-breaking.

Even with that. It's anonymous if you don't login. All you do is pick a name you like, type something random and exit. And all they have is an ip address that may change at anytime.

I am not sure if GDPR should apply if that can't be used to trace back to you at first place.

And if this should apply. I think everyone on the earth that connect to internet are probably in danger. You visit my site and leave a message. And I am suddenly a target of GDPR, what?

Also, do GDPR actually care about internally logs? I think the requirement is the data on that platform can no longer be used to trace back to the user. But logs aren't even exposed to users.

yes GDPR care about internal data like logs, because companies get breached all the time and data get leaked.

Since GDPR, PII (Personal Identifiable Information) data has become radioactive, the less you touch it easier your life is.