This thread is resolved. Here is a description of the problem and solution.
We use the Composite Products plugin, and there is an options style, where we use "Thumbnails" to show the products in our original English language. In our second german language, the option style is set to "Dropdown".
I have solved the issue. I had to re-save all the products in the original English language, and after that, the option style was the same in the German language.
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