Mounted volume not accessible
Finally, after many turns, I've found what's going on:
The executing shell/app in the script (e.g. zsh, sh, python - in my case /bin/bash) needs to have Full Disk Access privileges. In order to do so I went to Apple Menu > System Preferences > Security & Privacy, selected Privacy tab, unlocked the settings and added /bin/bash to the list.
Now I can read and write the mounted share.