PII is a concept is US law. The GDPR uses personal data, defined as:
"any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, an online identifier or to one or more factors specific to the physical, physiological, genetic, mental, economic, cultural or social identity of that natural person"
Pseudonymization (separating unique identifiers from the rest of the datapoints) can and should be used as a safeguard, but doesn't remove the need to protect the data, particularly if you keep a link between the two.
"any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, an online identifier or to one or more factors specific to the physical, physiological, genetic, mental, economic, cultural or social identity of that natural person"
Pseudonymization (separating unique identifiers from the rest of the datapoints) can and should be used as a safeguard, but doesn't remove the need to protect the data, particularly if you keep a link between the two.