Energy transition narratives have intensified the convergence of fossil fuels, transition metals, and maritime shipping; however, market reactions remain asymmetric, with negative news spreading faster and persisting longer than positive developments. This study quantitatively examines this asymmetry by analyzing monthly (January 2003–March 2025) spillover effects among energy commodities (OIL, GAS, COAL), base metals (METALS), freight indices (BDI, BDTI, BCTI), and climate-related uncertainty indicators (Climate Policy Uncertainty-CPU; ESG Uncertainty-ESGUI). Using a TVP-VAR-based asymmetric connectedness framework, the analysis captures time-varying and direction-dependent transmission by decomposing shocks into positive and negative components. The results show that system-wide connectedness increases sharply during periods of global stress and that negative shocks generate stronger and more persistent contagion effects than positive shocks. CPU and energy prices occupy central positions in the network under adverse conditions, while ESGUI primarily acts as a receiver of information. Overall, the findings indicate that climate policy and sustainability uncertainty are not marginal signals but integral components of the volatility transmission network in energy, metals, and freight markets, particularly when markets price downside risks. These results suggest that uncertainty transmitted through energy and maritime shipping markets constitutes a critical risk channel for urban energy security and clean transportation systems. From a sustainability perspective, the asymmetric propagation of downside risks provides a quantitative foundation for incorporating uncertainty into decision-support frameworks for resilient urban infrastructure and energy transition planning.