Zero Google services are shippsx by default, but you can install Play Store and Services in a sandbox and it has minimal privacy problems, depending on the permissions you give it.

Their docs are really good, not only for their phone but for learning about privacy and security: https://grapheneos.org

You could still install an app that spies on you on grapheneos because it has 99.99% android app compatibility, so if you gave an app designed for spying the relevant permissions, it would still be able to spy. No way it could hide location indicator or anything like that, but I doubt it could do that on other OSes (don't quote me on other OSes).