From your description you are successfully able to receive the push notification when the app is in the foreground - that means that the device is registered correctly in Telerik Platform Backend services and that the push notification setup is also correct.
When the app is in the foreground, the received push notification are handled by the app code, more specifically by these functions here in Basic Push sample app.
When the app is in the background, the received push notifications are handled on operating system (OS) level. On some Android devices though, the apps are not permitted by default to stay awaken in the background due to a rather aggressive phone's battery optimization feature. This way the push notifications not processed when the app is not running and is forbidden to be awaken in the background. This additional functionality is added to the OS by the phone manufacturers and should be allowed on the device by the user.
Currently, this behavior is identified on devices from the following manufacturers:
You need to modify certain settings on your device.
- Open Settings → Protected Apps
- Place your application in the list
- On the app screen tap on the Security app
- Select Permissions → Autostart
- Locate your app in the list and enable "Autostart"
- Restart the device
- Locate the Auto-start Manager as noted here
- Locate your app in the list and enable "Allow"
Let me know if this was the case or if the problem persists.
As to your other question - Telerik Platform backend services is sending the push notifications to FCM (Firebase Cloud Messaging) but you would have to use Telerik Platform backend services Web portal or REST API endpoints to send push notifications.
I hope this has helped.