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This thread is resolved. Here is a description of the problem and solution.
Problem: Product category do not work properly when switching language. Some of them redirect to post pages, others return errors 404.
Solution: There are 2 separate issues: 1. For the category that redirects to a blog post, there is a 301 redirect. WPML does not create redirects so I'm not sure from where this comes from. I checked your .htaccess but there is nothing in there. In many cases, Yoast creates redirects but usually when it's deactivated they disappear. I'd suggest searching your Google console to see if you can find something there.
2. the problem might have been that some of the shop link were in German and others in English. To fix it, I did as follows: - went to Settings > Permalinks and deleted the Product category base permalink and saved. This reset the default permalink, in English - in WooCommerce > WooCommerce Multilingual > Store URLs I re-entered the German translation. Now you can see all links to categories are working fine in your staging site, so with these steps you should be fine on your production site too.