Is there a way to get the results the normal way via FullTextQuery, but letting the "sort job" for the database? Or is it only possible to sort via the "setSort"-method from the FullTextQuery object.

No that's not possible, a FullTextQuery needs to be sorted the full-text way; that's because there could be a lot of matches but using pagination only the needed subject for current page is loaded from DB: to define which entities will be loaded the sort must happen before the fetch-from-DB step.

thanks for the explanation.