Did you reboot after adding openhab to the sudoers? Have a look here.
What information is desplayed when you run the skript as user openhab?
sudo -u openhab Test_Sprachausgabe.sh
Does that run? if yes then you could try to, add a rule to display what is prompted when the skript is executed.
Bind an item to the output channel of your thing and log the returned information of the execution.
Somehow your file permissions changed when copying!
When you copy a file, you are creating a new file. So, its (new file) permissions depends on the current file creation mask, which you change via umask command. Read man umask for more information.
Use the -p option to preserve the permissions when you copy a file or set the permissions afterwards.