Coordinated campaigns frequently exploit social media platforms by artificially amplifying topics, making inauthentic trends appear organic, and misleading users into engagement. Distinguishing these coordinated efforts from genuine public discourse remains a significant challenge due to the sophisticated nature of such attacks. Our work focuses on detecting coordinated campaigns by modeling the problem as a graph classification task. We leverage the recently introduced Large Engagement Networks (LEN) dataset, which contains over 300 networks capturing engagement patterns from both fake and authentic trends on Twitter prior to the 2023 Turkish elections. The graphs in LEN were constructed by collecting interactions related to campaigns that stemmed from ephemeral astroturfing. Established graph neural networks (GNNs) struggle to accurately classify campaign graphs, highlighting the challenges posed by LEN due to the large size of its networks. To address this, we introduce a new graph classification method that leverages the density of local network structures. We propose a random weighted walk (RWW) approach in which node transitions are biased by local density measures such as degree, core number, or truss number. These RWWs are encoded using the Skip-gram model, producing density-aware structural embeddings for the nodes. Training message-passing neural networks (MPNNs) on these density-aware embeddings yields superior results compared to the simpler node features available in the dataset, with nearly a 12\% and 5\% improvement in accuracy for binary and multiclass classification, respectively. Our findings demonstrate that incorporating density-aware structural encoding with MPNNs provides a robust framework for identifying coordinated inauthentic behavior on social media networks such as Twitter.