I could solve it. Our Joomla is set to “DE-CH” and this is why the language was not found. I copied and renamed the files from DE-DE to DE-CH and it works now.
IMHO opinion you can use the files from DE-DE also for other versions of DE – DE-CH and DE-AT or “DE-COMMON” (if it exists). There is no reason to limit it to DE-DE.