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With the rapid growth of online grocery retail, firms are increasingly focusing on shaping demand through dynamic product displays (i.e., ranking and assortment decisions). However, this introduces several intertwined challenges, such as tailoring product displays to evolving inventory levels and managing quality decay among products of varying ages. Beyond these operational complexities, sustainability concerns create additional pressure to curb food waste and improve societal outcomes. We propose a unified framework for online grocery retailing that explicitly incorporates these operational and environmental interdependencies into the coordination of inventory and display decisions. We introduce a novel approach that can be systematically transformed to recover the optimal policy of the fluid version of the stochastic problem and further construct an asymptotically optimal policy for the original stochastic system based on the optimal fluid solution. The optimal solution can be computed in polynomial time with respect to the number of products. Moreover, we show that under the proposed policy, only minimal daily adjustments are required, and display lengths vary by at most one unit, which ensures a stable and smooth browsing experience for customers. Beyond the theoretical results, a full welfare analysis comparing firm profit, waste, and customer surplus across different policy regimes (waste ban vs. no ban) and operational strategies (static vs. adaptive) shows that our adaptive display policies outperform static policies across all dimensions, yielding higher profit, lower waste, and higher customer surplus. They hence provide a rare win-win-win framework in public policy design. Our numerical simulations further reveal that adaptive display policies can render organic waste bans nearly redundant or even counterproductive: with adaptive systems in place, bans yield negligible additional waste reduction while introducing inefficiencies (lower profits) and compliance burdens that increase regulatory costs.