I saw on the GrapheneOS forums that some people had managed to get it working, but I was unable to do so.

My bootloader is locked, because I re-locked it after installing GrapheneOS. The app runs, but refuses to let me log in. I even tried (temporarily) using a browser to login, and let the browser switch to the app in the process. Nada.

It's ridiculous that Google bills their "DEVICE INTEGRITY" initiative as a security feature, when GrapheneOS, which is a more secure platform, cannot use it.

Hmmmm.... Actually you can have an unlocked bootloader for the basic integrity level.[0]

[0] https://developer.android.com/google/play/integrity/verdicts