Galaxy clusters are the largest gravitationally bound structures in the Universe, serving as key laboratories for studying structure formation and evolution. The intracluster medium (ICM), composed of hot plasma, dominates their baryonic content and is primarily observable in X-rays. The thermodynamic properties of the ICM, including pressure, temperature, entropy, and electron density, provide crucial insights into the physical processes shaping these systems, from accretion and mergers to radiative cooling and feedback. We investigate the thermodynamic properties of galaxy clusters within the Simulating the LOcal Web (SLOW) constrained simulations, which reproduce the observed large-scale structure of the local Universe. Our goal is to assess the reliability of these simulations in reproducing the observed ICM profiles of individual clusters and to explore the connection between cluster formation history and core classification. We extract three-dimensional thermodynamic profiles from the simulations, assuming spherical symmetry. These profiles are directly compared to deprojected X-ray and Sunyaev–Zel’dovich (SZ) observational data for a sample of local clusters, including systems classified as solid cool-core (SCC), weakly cool-core (WCC), and non-cool-core (NCC) systems. Additionally, we analyze the mass assembly history of the simulated cluster counterparts to establish links between their formation pathways and present-day ICM properties. The simulations successfully reproduce the global thermodynamic profiles of observed clusters, particularly in the pressure and temperature distributions within r500. The electron density and entropy profiles of cool-core (CC) clusters show some discrep- ancies, likely due to resolution limitations and the treatment of feedback processes. We find that CC clusters typically assemble their mass earlier, while NCC clusters experience more extended merger-driven growth. WCC clusters exhibit intermediate accretion histories, suggesting an evolutionary transition between CC and NCC states. Our results demonstrate that constrained simulations provide a powerful tool for linking cluster formation history to present-day ICM properties. While the large-scale structure and bulk thermodynamic profiles are well reproduced, further refinements in subgrid physics as well as higher resolution are needed to improve the agreement in cluster core regions. These findings offer new insights into the evolution of cluster cores and their observational classification, reinforcing the importance of constrained simulations for studying galaxy clusters in a cosmological context.