How to link grouped Products?

Hello WordPress Community,

this is the first time for me using this forum so please have indulgence and i hope that you will be able to help me.

The problem in short:

As for the site, I want to group different products by manufacturer. The native WordPress Product-Option “Grouped Products” is pretty much exacly what i am looking for. This would mean I have a Group product, which then contains all the single products linked to the group product.

As far as my research goes, all i would have to do, is:
1.: set up the grouped product
2.: Link all single products to the grouped product.
You can see the result of this grouped product here:
https://flaschenfalke.de/produkt/reissdorf-koelsch-gruppe-test

3.: Now, according to my research, i would need to go into all the single products which are part of the group, scroll to the “linked products” section and use the option “Grouped products” to then connect the single product back to the group.

Now here is the problem:
I can’t see the option “grouped products” in the single product>linked products options. All i can set in there is “Up-Sells” or “Cross-Sells”

I think this is the reason why the grouped products are not working. If I want to put a grouped product in the cart, it won’t work. If I put the single product itself in the basket, it is working just fine.

Any help is appreciated. Thanks

The page I need help with: [log in to see the link]