SMS and other notifications only appear when the desired app was recently launched

Describe the bug
SMS messages are never received if the SMS app isn't running in the background. SMS doesn't get to the 'mailbox' and is lost forever. Opening the app later does not make it appear.
When the SMS app is running, the messages are always delivered.
Tested with QKSMS and Simple Message.

Push notifications don't work either unless the desired app is running.

To Reproduce
Steps to reproduce the behavior on Asus ROG Phone 3:

1. Unlock the bootloader, make /system writeable and root the phone.
2. Debloat gapps and install microG with FakeStore through NanoDroid
3. Give microG all the necessary permissions, disable battery optimizations, enable signature spoofing...
4. Go through all microG self-checks to see they are now all green
5. Install an SMS app, or any app utilizing push notifications
6. See that after some time, no SMS or notification is received unless the target app was already running

Expected behavior
SMS and notifications never get lost

System
Android Version: 10
ROM: stock WW rom, debloated through NanoDroid

Additional context
NFC does not work either. Nfc cards never get detected by the phone. Google wallet is stuck on loading the 'choose Google account' popup

Start by reproducing the missing SMS and push-notification behavior using the Asus ROG Phone 3, Android 10, and the microG/NanoDroid setup described. Compare behavior with the target apps running and stopped, and include NFC as a separate symptom to determine whether the issue has a shared cause. Done means SMS and push notifications are delivered while the apps are stopped and are not lost.