I don’t think you need a Google account to use Sandboxed Play Services in general. Maybe some specific things that require you to be logged into the Play Store but overall I can use Android Auto and other things I need without being logged in.

What did you find you needed to be logged in for?

I’ve been using GrapheneOS on my phones since the Pixel 3 and I have not had this issue when using Verizon. For the other person maybe it was a different carrier? Or some issue a while ago with that carrier and GrapheneOS.