For the preferred binding site, we compute state energies and spin-related properties, including spin and orbital angular momentum, and SOC using EOM-CCSD-in-DFT on finite models of Co/MgO(001). The embedded EOM-CCSD method seamlessly integrates into the EOM-CCSD framework, granting access to all its variants, including excitation energy (EE), ionization potential (IP), electron attachment (EA), and spin flip (SF). This integration also enables the analysis of spin states and spin properties using reduced quantities, such as natural orbitals (NOs) and natural transition orbitals (NTOs). Beyond state energies and SOCs, we derive spin-inversion energy barriers and susceptibilities using a protocol that follows a state-interaction approach to treat relativistic effects and applies Boltzmann statistics for computing macroscopic properties. The accuracy of EOM-CCSD-in-DFT is assessed against EOM-CCSD, CC2, and experimental data. We show that for the preferred adsorption conformation of Co on MgO(001), DFT-based methods fail to predict the easy-axis magnetic anisotropy, providing a qualitatively incorrect description compared to experiments. In contrast, embedded EOM-CCSD accurately captures the multiconfigurational, non-aufbau nature of the spin states, yielding results that closely match experimentally derived magnetic anisotropy energy values, and thus highlighting the effectiveness of this embedding approach for describing magnetic adsorbates. Furthermore, by comparing Co adsorbed on MgO(001) with a linear, twofold-coordinated Co(C(SiMe 2 ONaph) 3 ) 2 single-molecule magnet (i.e., Co(II)-SMM), we establish a parallelism in their electronic structure and magnetic behavior. Both systems exhibit a nonaufbau ground state and strong magnetic anisotropy, demonstrating how electronic structures and magnetic properties can be replicated in different environments through carefully tuning the local coordination of the magnetic center.