Language switching not working

I am on Joomla 4.3.4 with PHP 8.1.26 in conjunction with a Maria-DB MySQLi 10.11.4-MariaDB-1:10.11.4 - Joomla-Caching = off completely

I just have bought the license for OS Services Booking and this are my first steps with this extension:
I want to use the German language and using the menu item "Translations" I have selected de-DE instead of en-GB. I could see the success in the fields of the translation table beyond. They were in German now. But the Language in the frontend showed a bad German translation (see screenshot attached)
When I went back to the menu item "translations" and controlled the setting "German", it was back to en-GB. It did a reset by itself! But more astonish: The language in the table beyond stayed to be German. I tried once again, choosing "language override". But I got the same result, as described before. It did reset itself to en-GB.

After that, I found many expressions to have a bad translation. So I decided, to translate the language files.
It is strange, that the English file and the German file have different length: The German ends at line 467 the English at line 631.
Then I translated the English language file to German and replaced the regular German language file in the folder .../language/de-DE. But when I tried to switch language to German like I described above, the German translation did not show up in the fields of the table below. It seemed, that no changes are accepted there!

Then I copied my German language file to the ../language/overrides folder and then did select Language = override. – Same problem as before. No changes in result.
It will keep the bad original German language from the first change, I made in the language selector

What should I do to get it work correctly?

Hi Martin,
Could you please submit ticket on category: OS Services Booking and provide your site credentials. We will check and help you to solve the issue with language files
Thanks
Dam