During troubleshooting, I noticed that the term field 'Einleitung-Produktkategorie' is of type 'WYSIWYG'. This field's content can be affected by the extra content processing filters, applied by the active theme and the third-party plugins.
WordPress offers a content filter 'the_content', which is used by WordPress, themes, and plugins to apply formatting and other processing to the long content sections, like post content body and description fields, such as the 'WYSIWYG' fields.
( ref: https://developer.wordpress.org/reference/hooks/the_content/ )
There are many plugins active on your website, so it won't be possible to say for sure. But most likely this extra processing was caused by the Elementor builder, as the archives are using the Elementor templates.
The use of the suppress_filters="true" attribute, ensures that the content of the field is returned exactly as saved in the database, without going through the filter 'the_content'. This means that it is a good practice to always use this attribute when the 'WYSIWYG' field is used in third-party page builders.
The only difference I noticed between the archives where the field was working and where it wasn't was that there were two archive templates from Elementor applied to the ones where the field wasn't working.
Thank you very much for the explanation and the info about the two aplied archive templates.
Can you tell me which two templates are applied or how you recognized it?
When you visit any page on the front end, you'll see a menu item from Elementor 'Edit with Elementor', in the top admin bar.
(when you visit logged-in as an administrator)
This lists which templates are being used for the current page.