As consumer demand for eco-friendly products continues to grow, manufacturers are increasingly driven to enhance product greenness and disclose this information. Blockchain technology emerges as a pivotal enabler, facilitating credible communication of manufacturers’ sustainability efforts to consumers through retail platforms and influencing supply chain decisions concerning sustainability, pricing, and blockchain adoption. While existing research has extensively examined the positive moderating effect of blockchain technology on consumers’ perceived value of product greenness in retail competition or green supply chain contexts, there remains a significant gap regarding its cross-channel influence in situations of information disclosure asymmetry across retail platforms. To address this gap, we investigate the interactive dynamics of a green supply chain under asymmetric platform competition, where the incumbent platform offers blockchain services while the new platform does not. Our findings indicate that the manufacturer’s decision to adopt blockchain depends significantly on market conditions. Notably, the manufacturer’s inclination towards blockchain adoption widens for a broader range of blockchain costs when the cross-channel influence is pronounced. Moreover, the alignment of the manufacturer’s blockchain adoption strategy with the incumbent platform’s preference is not guaranteed. In scenarios where their interests diverge, joint efforts to reduce blockchain costs can be a viable strategy. Our parametric analysis further reveals that while the cross-channel influence contributes positively to enhancing product greenness and the manufacturer’s profit, it could diminish the profits of both platforms under certain conditions.