Malternative What I was wondering with my second point was mainly for example how the app will behave when I'm in a different profile than the app is running in (though I'm not sure if that would work even on stock android)
GrapheneOS has expanded support for multiple user profiles. They also fixed many privacy leaks (apps running on different profiles are not supposed to be able to communicate with each other in any way, although there still remain some leaks). See:
https://grapheneos.org/features#improved-user-profiles
I personally think the multiple user profile feature is overrated. It has many non-obvious issues. I'd personally recommend you to stick to simply using one user profile for everything, it could save you lots of headaches later.
Malternative how it handles stuff like overriding silent mode with custom ring tones
You can set any app's notification channel to bypass Do Not Disturb/Modes, and give it a custom notification sound.
Malternative at custom volumes
I'm not aware of such a feature. Maybe you could achieve it with the help of an app, idk.
Malternative appearing on top of everything else
You can grant any app the Display over other apps special permission, however this is an incredibly dangerous permission with non-obvious security risks, so you should try to avoid granting it, to any app (not just this app).
Malternative (and on the lock screen)
You can grant it the Full screen notifications special permission. This is kind of a silly name, it's a permission to display activities over the lock screen without having to unlock. So if the app needs to pop up an alert for you, it could do it with this permission.
Note that if the app doesn't support Android's Direct Boot mode, you will still have to unlock your phone at least once after every time you reboot it/power it on, even with this permission. This is not a restriction that GrapheneOS added, this is how it is in stock Android. (Do note that GrapheneOS adds an auto-reboot feature, that automatically reboots the phone when it's locked and not being used for a certain consecutive period of time (i.e. the countdown resets when you unlock), by default 18 hours. You can also disable this feature.)