Disclaimer: Please do not read this as "demanding", but rather as trying to understand:
Dumdum
This is not about "I want my favorite app", this is about providing basic functionality that cannot be achived by just installing the app manually. I don't really care whether it is Neo Backup or something else. oandbackup (MIT License!, "mother" of Neo Backup), or Swift backup (well, closed source I guess) should be fine, too. I just mentioned NeoBackup because that is the one I used before.
"GrapheneOS is focused on making meaningful improvements to privacy and security" - backup and restore is (part of) security
The "We plan on replacing it with a new implementation since the project has been taken over by another group of people not sharing our goals or approach." is written in that FAQ since May 2022!
You do such a great job in implementing dozends of additional security techniques, it just seems odd that this seems to have such a low priority. This rather simple functionality (basically: copy data to encrypted archive and back) is "coming soon" since more than 2.5 years.
Would some kind of "if apk is named xyz and signed by original autor grant required permissions for backup" an option? Like a su but the OS maintainer decides which app is allowed to and not the user? (maybe with a default-off toggle in the settings for users that dont want to use it or only occasionaly)
that way the ROM would not have to include the AGPLv3 apk of NeoBackup but still it can be used.
Thanks for reading