Thank you Julius, I think I have found the issues.
1. The post contents are indeed very large, but the extra text is wrapped in the [hide] .. [/hide] shortcodes. When the plugin tried to idnex that, the shortcode execution simply removed that whole part – all of the keywords. I have added an exception for that shortcode here: https://i.imgur.com/ZtzmxhS.png
The index size grew from 15k keywords to 335k, which seems to be correct.
2. The pool size values were also set incorrectly, I have changed that back to the default: https://i.imgur.com/qYSvnUt.png
Now, searching “waschmaschine” or any other keyword should give you the expected results.