only to ask for permission in the blocks does not help very much without the permission in the manifest...
Be aware that this permission is usually not granted by Google.... ler's assume, you do not plan to publish your app in Google Play...
without permission MANAGE_EXTERNAL_STORAGE:
what kind of files are you trying to pick? media files or non media files? created by your app or other apps? see also the overview here Some basics on Android storage system - #34 by Anke
and use SAF to pick non media files created by other apps