Is using a IP logger Illegal?

Capturing someone else's IP address is like using caller ID. It is not picking up confidential information. It also has nothing to do with Intellectual Property (also called IP, but not related).

In your context, IP with nothing more corelated is like a phone number. When one connects to the Internet, he has no reasonable expectation of privacy of his IP. Anyone may log others IP. (like phone call log or call history). Anyone may sniff IP of others if one has full rights to the network device or the LAN (unless there is a prior agreement assuring privacy on the Network). You can also force your ISP or website to give you a new IP by changing your Hardware/Host address (e.g. MAC address). Now, using another IP address (IP spoofing as another) is a different matter and could trigger federal and state computer crime (and ISP TOS/contract violation) liabilities.

Here is a prior answer on which may or may not be helpful. https://www.attorneyqna.com/legal-answers/is-it-legal-to-have-someones-ip-from-an-ip-logger-2551217.html You should discuss with an attorney in a private consultation.