Local log files are not automatically compliant by my reading of the GDPR, but IANAL. My understanding is that PII is a huge risk, regardless of it being local

Local log files are not automatically compliant by my reading of the GDPR, but IANAL. My understanding is that PII is a huge risk, regardless of it being local or with a vendor, and you aren't allowed to track things that you aren't actively using for some business process. Many default log formats have data that people don't actively use, which seems to be a violation of GDPR even for local files. Again, IANAL.