The no hair theorem says that black holes rapidly converge to a state that is completely described just by their mass, spin and charge. Black hole thermodynamics says that the black hole entropy is proportional to the surface area of the event horizon. As I understand it in information theoretic terms the black hole entropy is 1 bit per planck unit of area, which should then be the amount of information required to fully describe a black hole. These two statements seem to be incompatible. It seems that the thermodynamics says that if we fix the macroscopic no hair parameters there still remain all the surface bits to be fixed. Is there any real conflict here or is somehow illusory? Is it a quantum vs classical issue? Does the entropic information not count in some sense? If not why, can 2 equal mass Schwartzchild black holes be distinguished by their "surface information"? Is it that the surface information is just not observable because the surface is considered in the black hole? Or is this apparent discrepancy part of the black hole information paradox?
There is a very similar question with a detailed answer here, but I believe I am actually asking something different. The question and excellent answer there focus on the objects as they fall into a black hole. I am more interested in how to think about the total information in a steady state black hole and the current status of the no hair theorem wrt black hole entropy and the information paradox.