IP is technically PII in some places. Personally I am not worried if a criminal gets "my" IP in the same way that I am not worried if they have my phone number. I would be worried if they had my name address age bank account info etc, but then I don't give that out freely
That's not the definition of PII. At best, that covers a small subset of PII.
PII means any information that can be used to identify you, either directly or indirectly.
When you access a website combined with which link you opened or which search keywords you used can be used to infer who you are.
How do you tell if a script is not shipping that info to an undisclosed third-party?
That's kind of my very coarse litmus test for PII: If I'm not willing to post it publicly in a rando internet forum, it's probably PII. There are exceptions obviously, and the inverse is not true: I may be willing to publicly post certain PII.