Yes, a blog cannot claim to be "purely for personal or household use" because it is an online publication and so the GDPR applies.
I think you are falling down the "GDPR rabbit hole" here, though. As said, for a personal blog the most probable scenario is that no-one will care about your following the law strictly to the letter.
Now, you can reasonably argue that you have a legitimate interest in logging IPs and to keep them for a sensible duration for security audit purposes. So in any case, you can just inform visitors that you will log IPs for security/spam prevention purposes and move on.
Commenters do not necessarily have a right of erasure and as you have said you probably won't be able to check that requests are genuine, anyway. So I think a sensible approach is not to worry about that until and unless you receive such a request and then decide what to do to make your life the easiest possible. For instance, if one day someone claims to be the author of a comment and wants it deleted you might decide to just delete it and to move on whatever the strict legal position and procedure might be.