Exec-Binding on Paper UI with openHAB2

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.

String exec_Out { channel="exec:command:< YOURTHING>:output" }
rule "Exec Prompt"
  when
    Item exec_Out changed 
  then
      logInfo("Exec prompt", "\n" + exec_Out.state +"\n" )
end

You can then see the output in the log files or in the karaf console.