Pixel phone privacy. How to exempt data sharing with google
You will need to install another ROM that does not have Google Play services such as LineageOS or GrapheneOS.

I am also not using any Google apps.

It does not matter which Google apps you explicitly use or not, this process is a core part of stock Android.

VPN is always active on the phone

This cannot be guaranteed unless the phone is rooted as some connections might be made before the VPN is setup.