I would not say there is any 'coupling constant' set anywhere. The strength of the coupling is indirectly encoded in the ionic potentials (VASP uses PAW).

In terms of the (simpler) norm-conserving pseudos, the action of the atomic core on a free electron is simulated by acting on the plane-wave with angular-momentum-dependent potentials. These are generated from all-electron calculations which may or may not include relativistic terms. If no terms, or only scalar terms, are included, L is a good quantum number and you get s, p, d, etc potentials. Including 'vector' terms such as spin-orbit, for each L you get twice as many potentials for up or down spin and your good quantum number is J. (These

The strength of the s-o coupling will show up indirectly in calculated quantitites. For example, the valence bands of group-IV insulators (C, Si, Ge) has a spin-orbit splitting increasing from a fev meV (can't remember now) in C to 50 meV in Si to 350 in Ge.

I am not aware of any "SOC constant" used in vasp. It's not clear to me whether you are asking about symmetry-dependent SOI (i.e. Dresselhaus interaction typically in bulk or Rashba interaction typically in surface) or symmetry-independent one (in atomic orbitals).