It appears as though targeting Android 15 in the future (if we want to be able to keep it published on the Play Store) will break functionality. This appears to be intentional, and this app won't fit the excluded "companion device manager" category. :(
https://developer.android.com/about/versions/15/behavior-changes-15#dnd-changes
https://developer.android.com/reference/android/app/NotificationManager#setInterruptionFilter(int)
I'll probably just pull the app from the Play Store at that point, keeping the APKs available under releases here on GitHub.