GrapheneOS inherits the user interface of the Android Open Source Project, which is what Pixels stock operating system uses, along with many other OEM forks of android.
GrapheneOSs App Store is present to fulfil the role of the first party appstore that AOSP requires. It also serves to provide updates to first party apps out-of-band, and mirror apps for various case-by-case reasons.
Accrescent is mirrored due to it having a focus on privacy and security. It is currently in alpha and app submissions are closed. They will be open Soon:tm:.
Google play is mirrored for app compatibility with apps that require google play, and for access to the playstore.
The GrapheneOS community favors Obtanium due to its ability to fetch developer-signed apps from places like Github. Fdroid signs and builds nearly every app on the main repository with outdated build infrastructure and poor moderation.
GrapheneOSs security model inherits and builds upon the AOSP security model.