Just chiming in to provide confirmation of configurations that work. I've been using Signal without issues for several months now, using the following configuration:
- Signal installed via Aurora Store
- Mullvad always-on VPN
- No Google Play Store installed (using WebSocket for push notifications)
- Permissions: Camera, Contacts, Microphone, Network, Notifications, Phone
- Battery profile: Optimized
- Alarms & reminders: Allowed
The last point is key, as Signal will not start automatically after a reboot unless this option is selected. This may explain why some users, such as @[deleted] seemingly lose push notifications after a time.
In my experience, Signal does not not require unrestricted battery access.