In your case, the bones of the decomposed rat may be causing a significant obstruction in the bend under the floor, which is why the sink is still draining slowly. A plumber may have a heavy-duty snake or hydro jetting equipment that can effectively remove the blockage.
It's also worth noting that if the blockage is located in a part of the pipe that is not easily accessible, a plumber may need to do some exploratory work to locate and remove the obstruction. This may involve cutting into walls or floors, which can be expensive and time-consuming.
Ultimately, the best course of action will depend on the severity and location of the blockage, as well as your budget and timeline. A plumber or drainage expert will be able to provide you with a more accurate assessment of the situation and recommend the most appropriate solution."