When the daily time limit is used up or the device blocking for the night is active, the children can simply open the desired app in a pop-up window and use it as long as they like. The "norton parental control" seems to be completely non-existent for apps that run in pop-up windows on Android 13.
Since there are several ways to open an app in a pop-up window, it doesn't help much to disable one of them in the settings. The other options remain. Among others, the simplest one - tap on the top icon of the app under "recent" and select "open in pop-up window" in the menu that appears.
The norton online protection for children on Android convinces me less and less. But I still hope and wait for a version that keeps what is promised.
I have since solved the problem with the free Google Family Link app.
The time limits and night rest are now set with it reliably working and without having to manually disable valid operating system functions.
Please follow these steps to prevent the child from accessing the Smart Pop-up View.
1. Open Settings on the child's device.
2. Go to Notifications > Floating Notifications.
3. Select "Off".
AND,
1. Open Settings.
2. Go to Advanced Features > Labs.
3. Ensure that the toggle button for all the features are turned OFF.
We also recommend you to block the Settings App under App Supervision so as to not allow the child to tamper with the above Settings. Feel free to refer this document for assistance in this regard.
Kindly be noted that in Samsung devices, an app can be launched in a pop-up window in more ways than one. The other way via recent apps is already handled by the Norton Family App.