Hi ssali,
If you need the products for exactly one category (not a category path) there is an easy way. You just need turn around you search. So instead of searching for products and check what category they are assigned to you can query the products of a category itself:
The api endpoint would be
POST https://shop.domain/api/v{version}/search/category/014c55d9156e40188f34b6b99e957069/products
This is also described in the shopware documentation.
Hope this helps you :)