Context. In a hierarchical Lambda CDM Universe, cosmic filaments serve as the primary channels for matter accretion into galaxy clusters, influencing the shape of their dark matter halos. Aims. We investigate whether the elongation of galaxy clusters correlates with the orientation of surrounding filaments, providing the first observational test of this relationship in large supercluster regions. Methods. We identified and characterized cosmic filaments in two dimensions within the two superclusters that are part of the low-redshift sub-survey of the Chilean Cluster Galaxy Evolution Survey (CHANCES): the Shapley supercluster and the Horologium-Reticulum supercluster. We analyzed the alignment between filament directions-traced by galaxy distributions-and the triaxiality of cluster gravitational potentials-traced by X-ray emission-using publicly available optical and X-ray data. Results We have found that most (82%) of the X-ray clusters are associated with and interconnected by the optically detected filaments. The clusters-filaments alignment analysis shows that the elongation of most clusters is well aligned with nearby filaments, providing observational confirmation of theoretical predictions, with the alignment progressively reducing at larger cluster-centric distances (> 1.6r(200)). Conclusions. Overall, our results support the notion that filaments are the main source of galaxy accretion at redshift below 0.1, and additionally provide evidence that matter accretion through filaments shapes the gravitational potential of galaxy clusters. We propose this measurement as a simple observational proxy to determine the direction of accretion in clusters, which is key to understanding both galaxy evolution and the merger history of galaxy clusters.