Hello,
first of all respect for such an achievement. A lot of work with good documentation and functionality! As a test I created the page: https://www.medewa-hygiene.de/testsuche/
I have following questions:
Can you deactivate all filters per group in the frontend with one click? Are everyone always active at the beginning?
I was having trouble with the search results page. The Divi Builder has a template for the search that I had to disable. Actually, the layout (Divi shop page): https://www.medewa-hygiene.de/artikel/ should be used.
I tried to check the page on the URL provided, but there is currently nothing on there.
If you are reffering to checkbox statuses (like checked unchecked) for taxonomy term filters, it depends on these settings here: https://i.imgur.com/MnEuQad.png