Open cavities are emerging as a promising platform for studying light-matter interactions. A lossy open cavity couples to an atomic monolayer, resulting in parabolic dispersive emission at room temperature. Here, light-matter interaction is weak, and the dispersion arises from a phenomenon known as dark strong coupling. The bright 2D exciton rapidly decays through the cavity mode, leaving behind spin-dark excitons of the 2D lattice, thereby undergoing symmetry breaking. Further, mapping the polarisation dependence in the k-space reveals spin-orbit interaction in the coupled system. A synthetic spin-orbit Hamiltonian is constructed to extract the effective contributions of Rashba- and Dresselhaus-type interactions in the open cavity. The system shows a clear evolution of the spin-orbit effect at room temperature. Here, emission is polarisation-sensitive, yielding high degrees of linear and circular polarisation. This is one of the simplest configurations for studying photonic spin-orbit coupling, in which an atomic monolayer provides Rashba and Dresselhaus coupling constants of 24 eV Å, and ~10^5 eV Å^2, respectively. Therefore, an open cavity platform is promising for polarisation-sensitive measurements and device applications.