Multiple cluster systems, that is superclusters, contain large numbers of galaxies assembled in clusters interconnected by multi-scale filamentary networks. As such, superclusters are a smaller version of the cosmic web and can hence be considered as miniature universes. In addition to the galaxies, superclusters also contain gas, which is hot in the clusters and warmer in the filaments. Therefore, they are ideal laboratories to study the interplay between the galaxies and the gas. In this context, the Shapley supercluster (SSC) stands out since it hosts the highest number of galaxies in the local Universe with clusters interconnected by filaments. In addition, it is detected both in X-rays and via the thermal Sunyaev-Zel'dovich (tSZ) effect, making it ideal for a multi-wavelength study of the gas and galaxies. Applying for the first time a filament-finder based on graphs, T-REx, on a spectroscopic galaxy catalogue, we uncovered the 3D filamentary network in and around SSC. Simultaneously, we used a large sample of photometric galaxies with information on their star formation rates (SFRs) in order to investigate the quenching of star formation in the SSC environment which we define as a function of the gas distribution in the Planck tSZ map and the ROSAT X-ray map. With T-REx, we confirm filaments already observed in the distribution of galaxies of the SSC, and we detect new ones. We observe the quenching of star formation as a function of the gas contained in the SSC. We show a general trend of decreasing SFR where the tSZ and X-ray signals are the highest, within the high density environments of the SSC. Within these regions, we also observe a rapid decline in the number of star-forming galaxies, coinciding with an increasing number of transitioning and passive galaxies. Within the SSC filaments, the fraction of passive galaxies is larger than outside filaments, irrespective of the gas pressure. Our results suggest that the zone of influence of the SSC in which galaxies are pre-processed and quenched is well defined by the tSZ signal that combines the density and temperature of the environments.