This study delves into the role of process awareness in enhancing intrusion detection within Smart Grids, considering the increasing fusion of ICT in power systems and the associated emerging threats. The research harnesses a co-simulation environment, encapsulating IT, OT, and ET layers, to model multi-stage cyberattacks and evaluate machine learning-based IDS strategies. The key observation is that process-aware IDS demonstrate superior detection capabilities, especially in scenarios closely tied to operational processes, as opposed to IT-only IDS. This improvement is notable in distinguishing complex cyber threats from regular IT activities. The findings underscore the significance of further developing sophisticated IDS benchmarks and digital twin datasets in Smart Grid environments, paving the way for more resilient cybersecurity infrastructures.