Accessing Android NotificationListenerService Settings

Additional to CommonsWare answer here is how to check if you have that permission

if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.JELLY_BEAN_MR2) {        
    if (!NotificationManagerCompat.getEnabledListenerPackages(this).contains(getPackageName())) {        //ask for permission
       Intent intent = new Intent("android.settings.ACTION_NOTIFICATION_LISTENER_SETTINGS");
       startActivity(intent);
    }
}

Am I missing something?

Well, in your last one, you are conflating an action string with a class name. The "manual" approach would be:

Intent intent=new Intent("android.settings.NOTIFICATION_LISTENER_SETTINGS");

In terms of why Android Studio is not finding Settings.ACTION_NOTIFICATION_LISTENER_SETTINGS, that I can't say.

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UPDATE

Based on the discussion in the comments, Settings.ACTION_NOTIFICATION_LISTENER_SETTINGS is not in the Android SDK at present (marked with @hide). Also, the manifest for the Settings app has a slightly different version of the action string:

Intent intent=new Intent("android.settings.ACTION_NOTIFICATION_LISTENER_SETTINGS");