Yes, that is point-wise constraint where at the shared boundary \Omega_1\bigcup\Omega_2 we have \kappa\nabla u \cdot \pmb{n} = FD\nabla c \cdot \pmb{n}. (Otherwise, my reading of Allocating different variables to different subdomains - #2 by dokken convinces me that the problems are related.)
I will post my MWE. I believe I have the variation correctly defined for the constraint but have arity issues while computing the Jacobian.