>>Adriaa+(OP)
"We don't use cookies or collect any personal data."
IP-address is considered personal data. So when the browsers visits a page with the JS, the IP-address of the user is transferred to your server. So that means the website I am visiting is sharing my IP-address with a third-party (you).
>>xrisk+ba
I don't think that is relevant. What matters is that it is transferred to a third-party. And regardless if it is stored in a database, the servers are still processing the data (and maybe storing the log of it).
>>sleepy+sa
At least under GDPR the relevant question is if it is stored and who it is shared with. So if it is not stored/shared then it should be fine legally.