Hello is it possible to somehow create one more of the category picker for the product page in the backend. i would like to use it to create a function like related categories for each single product.
The short answer is "yes", is possible. :-)
I know is a (more) complicated control element but looking at Google I've found an example: https://belvg.com/blog/a-category-chooser-in-magento-2-backend.html
(I didn't tried but you can do your own I+D)