I would add:
- The user is logged in on multiple devices
- in the same state of the device and app
- in the different state of the device and app
- different type of devices (hardware, OS )
- The user receives before/after/at the same time notifications from other apps
Also I would try to figure out how much of this is OS related and how much depends on the app.
Do not test too much what is basic OS stuff.