Each operating system has a different level of compatibility.

GrapheneOS (Completely De-Googled): Every app available on F-Droid will work, since these apps are fully open-source. Proprietary applications like those available on Aurora may or may not work depending on their dependence on Google Play Services.

CalyxOS (microG): All apps available on F-Droid, and the majority of proprietary applications available on Aurora will be supported with microG’s replacement for Google Play Services.
Lookup compatibility for specific apps: https://plexus.techlore.tech/