> In certain larger EU countries you're not even allowed to record a website visitor's IP address (because some court has decided those count as PII)

You’re not allowed to do that without reason. If you have a reason, and tell your users, there’s nothing wrong with it.

Some anecdata that proves that:

https://gdpr.eu/privacy-policy/:

“IP and browser user agent string: this data is collected when you leave a comment.”

https://commission.europa.eu/privacy-policy-websites-managed...:

“In addition, IP addresses and device IDs might be saved for one year in the log files of the Directorate-General for Informatics operational environment for security or other purposes (see DPR-EC-02886 DIGIT IT security operations and services for more information).”