The +1/2 parameters are fixed and atom-specific, not environment-dependent. However, that doesn't mean that the +1/2 method itself is environment-agnostic; the self-consistent density and potential do enter into the integrals. If you had to adjust the parameters self-consistently, it would make the method unbearably slow and probably wouldn't even change the results much. One can actually see a parallel in DFT itself, where the pseudopotentials do not depend on the environment but the DFT calculation as a whole does, or for another example we use the same pseudopotentials for all different flavors of GGA functionals, although in theory one could attempt to find a specific pseudopotential (and then basis set) for PBE, revPBE, and so on. But these are the things we avoid in order to make DFT a practical method.
