We investigate the two-dimensional harmonic oscillator for a spin-1/2 particle using the Pauli equation in a \((2+1)\) -dimensional topologically charged Perry-Mann-type wormhole spacetime with cosmic string-type disclinations. The angular component of the Pauli spinor is a two-component plane wave. The radial differential equation includes relativistic corrections through spin-orbit coupling terms and the Darwin term. We derive the exact radial wave function expressed in terms of the Heun polynomial, along with the quantized energy levels and oscillation frequencies, incorporating corrections from spin-orbit coupling, the Darwin term, and topological effects in all cases. Furthermore, we investigate the effects of the cosmic string, global monopole, and spacetime curvature by graphically analyzing the eigenenergies and radial probability density.
