I am trying to make the normal map to work together with my displacement map, but it looks like one overrides the other or something like that, here is my node setup:
This has also been my experience. The normal map seems to always override the displacement map. If you are not using actual displacement of geometry, try using displacement map as bump map. However there have been many times where the same texture used with bump node looks very inferior to using it as displacement set to bump.
Does the displacement work if you disconnect the normal map? Are you sure you’re rendering with Cycles render preview and not material preview (top right in the viewport header)?
Can you plug the normal map into the displacement node normal input? My last resort would be to update to 3.2 if possible. Or maybe try the experimental feature set? Just shooting from the hip here.