Hey JBW,
I have found my problem. It was another override that I have tried to use before. This was causing the problem. Now I set everything to the original Prestashop files and used your provided file as a new override and deleted the classes_index.php. And voilà your solution works like a charme!
Thank you very much for your help!
As you can see in the example, the picture before was blurred. And before with the same compression the picture had almost 200kb. Now it looks better and it has only about 140kb.