Some time back, I had a similar problem: the LineageOS Messaging app was frequently late with SMS notifications when the phone was in idle state. Adding the package to Android's deviceidle whitelist fixed it right up. (This was done with the dumpsys shell command, since the setting for com.android.messaging was not exposed in the GUI.)

https://source.android.com/docs/core/power/app_mgmt#testing-...

I wonder if this setting could help Briar, and if so, whether an equivalent could be built in to their app packaging so users wouldn't have to fiddle with it.