Hi!
The problem is that the keyword ‘wohnzimmer’ does not match ‘Wohn- & Esszimmer’ in any way. However, I believe there is a much easier solution. On the category editor screen, you can enter a term description. I suggest using that field to enter the full name of the term: https://i.imgur.com/AC23eHo.png
After that, just make sure that the search in term descriptions option is enabled: https://i.imgur.com/bhcuosg.png
This should very likely do the trick.