Once it is approved it shouldn't be asked again.
Sorry, then we misunderstood each other. After each complete deinstallation and new installation, the system only asked me twice for permission out of the 10 installations. In principle, this should happen after every new installation that has been uninstalled beforehand.
Now i made some more tests. The Galaxy A53, which worked fine under Android 12 get's an update to Android 13 and after that, there are the same different behaviors as under the galaxy fold 3:
After the fist app start (after installation), the notification is set to not allowed by default. Only when a message arrives, the app asked the user, whether it is allowed or not. So the first message will not show an notification and it is a strange behavior, since the query may not come until days after the installation.
This is the behavior, when the targetdk is set to 31.
I made round about 50 installations and deinstallations and a few times, the app asked for permission only one ore two times at the first start of the app, all the other installations, the permission is asked after the first push arrives.
If i set the targetsdk to 33, the device does not asked if notifications are allowed and under settings there is no entry for notifications. So it is not possible to set it manually. The app also is not able to receive notifications under Android 13 and targetsdk 33.
(All messages will be arrived in Sub fm_MessageArrived (Message As RemoteMessage) in the logs. But not possible to set a notification.)
But as said, only under android 13.