I’m still working on getting my pixel set up but a lot of GOS users also use eSIM. I think you have to install a couple of google apps to fulfill some esoteric dependencies to make it work, but I don’t think you need to sign in to them or anything and if you do it over Wi-Fi with a solid vpn and via a good app repository, I don’t think google will actually learn anything about you/your new phone? Not totally positive about that.
That being said, Verison is infamously hostile towards respecting privacy. Hostile. They don’t merely refuse to help privacy, they actively try to screw everyone out of having privacy. So… yknow. Might wanna balance signal quality/coverage versus carrier shenanigans.
That also being said, all phone carriers are inherently trackers because that’s just how calling phones and using data works on cellular networks - they gotta know where you are to get the info to you or to beam the phone call at you or whatever.
There are services out there that do the best they can to mitigate this like Silent Link, or you can go whole hog and get one of those mobile hotspot routers that can be hacked to change their IMEI (a number that is irrevocably hardcoded to all phones nowadays)
I’m not saying you have to or should, I’m just trying to paint a picture of the spectrum available to you: anything between “just straight up use Verizon, or some Verizon MVNO” to “hacking the firmware or whatever of a mobile hotspot doodad and put your eSIM on it instead of on your phone”. GOS can work pretty much everywhere in that spectrum.