Developer-Dude There's no anonymous way to use it without sacrificing usability and even then I doubt it would even be anonymous then. GrapheneOS is for privacy–I don't think you should try to force someone to have anonymity as that's way harder than privacy.
I install WhatsApp from their website / using Obtainium because everyone that's complained about getting banned has installed it from Google Play (afaict). I don't think that's a big issue but why not show WhatsApp people want to get it from not the playstore, anyway.
You don't need play services except for notificiations.
Minimal permissions to just message on WhatsApp:
Network
What you need for a full experience:
Camera, for taking pictures in the app or video calling
Contacts and accounts (this is optional because whatsapp has an internal contacts system but if you want your phone contacts) can use storage scopes to choose which.
Microphone, for calling
Notifications, for notifications
Phone, so whatsapp knows there's no other calls happening on the device. This is not necessary at the technical level but WhatsApp doesn't allow calling without granting this permission.
Not allowed:
Call logs
Location
Music and audio (storage scopes)
Photos and Videos (storage scopes)
Sensors
SMS (this is absolutely not a necessary permission)
If it's for someone else I wouldn't use scopes of anything for usability problems.