What personal information do you think the VPN is blocking? Like, exactly. Precisely what information do you believe the VPN prevents a website from seeing about you?
I understand the difference between first and third party cookies. You said you were trying to prevent the website from tracking you. A website’s cookie for its own domain is first party. If you block that cookie, it’s harder for them to track you, and also you can’t log in.
Your IP address is not very useful for tracking you.
Residential IP addresses change often.
They’re usually shared by a family or organization through NAT.
You will often have different IP addresses throughout the day as you switch between WiFi and cell data.
Your different devices may or may not share an IP address.
The major ad trackers use cookies and etags to track you. They don’t use your IP address.