Google Mobile Services apps installed on GrapheneOS including Play services run as regular sandboxed apps. They receive absolutely no special access compared to other apps by installing and running them. There are the standard permission toggles for granting those but none of those are required for typical usage to provide compatibility with many apps from the Play Store depending on their services.

There are additional special permission toggles for RCS and Android Auto. The issue with RCS is mainly that they split the implementation across Google Messages and Play services. Android's standard permission model gives special access to the app selected by the user as the messaging app but Google Messages expects Play services to have special access too.

The shims defined with GmsCompatConfig are a small subset of the overall compatibility layer. It has many shims which need to actually implement the functionality such as remapping the Play Store using privileged installation APIs to the regular ones available to user installed app stores. It has to remap the APIs used by dynamite modules to ones not requiring privileged SELinux policies too. It has a mix of shims which simply stub out the functionality and many which need to handle it as a regular sandboxed app would need to do it.